Publications by Anthony W. Knapp
NOTICE:
The PDF files of articles on this webpage are intended only for
nonprofit educational and scientific purposes. Their inclusion
here is to expedite the traditional colleague-to-colleague sharing of
individual reprints and preprints of papers. Downloading of these
papers for any other purpose may run afoul of the rights of a publisher
under the copyright law.
Below is a list of my publications---books, articles, and other
writing.
Skip to: 1964 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 | 2010 | Book reviews | Other writing.
Books and articles
- Distal functions, Proceedings of the National Academy of
Sciences of the USA 52 (1964), 1409-1412.
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- Connection between Brownian motion and potential theory,
Journal of Mathematical Analysis and Applications 12 (1965),
328-349.
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- Regular boundary points in Markov chains, Proceedings of
the American Mathematical Society 17 (1966), 435-440.
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- (with J. G. Kemeny and J. L. Snell) Denumerable Markov
Chains, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1966.
Access to the table of contents
and the preface.
- Decomposition theorem for bounded uniformly continuous functions
on a group, American Journal of Mathematics 88 (1966),
902-914.
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- Distal functions on groups, Transactions of the American
Mathematical Society 128 (1967), 1-40.
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- Fatou's theorem for symmetric spaces I, Annals of
Mathematics 88 (1968), 106-127.
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- Doubly generated Fuchsian groups, Michigan Mathematical
Journal 15 (1968), 289-304.
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- Functions behaving like almost automorphic functions,
Topological Dynamics, an International Symposium, J. Auslander and
W. Gottschalk (ed.), W. A. Benjamin Inc., New York, 1968, pp. 299-317.
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- (with P. J. Kahn) Equivariant maps onto minimal flows,
Mathematics Systems Theory 2 (1968), 319-324.
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- (with E. M. Stein) Singular integrals and the principal series,
Proceedings of the National Academy of Sciences of the USA 63
(1969), 281-284.
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- (with E. M. Stein) The existence of complementary series,
Problems in Analysis, a Symposium in Honor of Salomon Bochner, R.
C. Gunning (ed.), Princeton University Press, Princeton, New Jersey,
1970, pp. 249-259.
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PDF.
- (with E. M. Stein) Singular integrals and the principal series
II, Proceedings of the National Academy of Sciences of the USA
66 (1970), 13-17.
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- (with E. M. Stein) Intertwining operators for semisimple groups,
Annals of Mathematics 93 (1971), 489-578.
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- (with R. E. Williamson) Poisson integrals and semisimple groups,
Journal d'Analyse Mathématique 24 (1971), 53-76.
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in PDF.
- (with E. M. Stein) Irreducibility theorems for the principal
series, Conference on Harmonic Analysis, Lecture Notes in
Mathematics 266 (1972), Springer-Verlag, New York, pp. 197-214.
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- Bounded symmetric domains and holomorphic discrete series,
Symmetric Spaces, W. M. Boothby and G. L. Weiss (eds.), Marcel
Dekker Inc., New York, 1972, pp. 211-246.
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- (with K. Okamoto) Limits of holomorphic discrete series,
Journal of Functional Analysis 9 (1972), 375-409.
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- Determination of intertwining operators, Harmonic Analysis
on Homogeneous Spaces, Proceedings of Symposia in Pure Mathematics
26 (1973), American Mathematical Society, Providence, Rhode Island, pp.
263-268.
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- Commutativity of intertwining operators, Bulletin of the
American Mathematical Society 79 (1973), 1016-1018.
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- (with R. Harvey) Positive (p,p) forms, Wirtinger's inequality,
and currents, Value Distribution Theory, Part A, R. O. Kujala
and A. L. Vitter (eds.), Marcel Dekker Inc., New York, 1974, pp. 43-62.
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- (with E. M. Stein) Singular integrals and the principal series
III, Proceedings of the National Academy of Sciences of the USA
71 (1974), 4622-4624.
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- A Szegö kernel for discrete series, Proceedings of the
International Congress of Mathematicians, 1974, 2 (1975), Canadian
Mathematical Congress, 99-104.
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- Weyl group of a cuspidal parabolic, Annales Scientifiques
de l'Ecole Normale Supérieure 8 (1975), 275-294.
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- (with E. M. Stein) Singular integrals and the principal series
IV, Proceedings of the National Academy of Sciences of the USA
72 (1975), 2459-2461.
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- Commutativity of intertwining operators II, Bulletin of the
American Mathematical Society 82 (1976), 271-273.
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- (with J. G. Kemeny and J. L. Snell) Denumerable Markov
Chains, second edition, Springer-Verlag, New York, 1976.
Access to the table of contents
and the two prefaces.
- (with E. M. Stein) Intertwining operators for SL(n,R),
Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann,
E. H. Lieb, B. Simon, and A. S. Wightman (eds.), Princeton Series in
Physics, Princeton University Press, Princeton, New Jersey, 1976, pp.
239-267.
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- (with N. R. Wallach) Szegö kernels associated with discrete
series, Inventiones Mathematicae 34 (1976), 163-200, and 62
(1980), 341-346.
Reprint of article in PDF.
Reprint of correction and addition in PDF.
- (with G. Zuckerman) Classification of irreducible tempered
representations of semisimple Lie groups, Proceedings of the
National Academy of Sciences of the USA 73 (1976), 2178-2180.
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- (with G. Zuckerman) Classification theorems for representations
of semisimple Lie groups, Non-Commutative Harmonic Analysis,
Lecture Notes in Mathematics 587 (1977), Springer-Verlag, New York, pp.
138-159.
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- Irreducible tempered representations, Lie Theories and
Their Applications, Proceedings of the 1977 Annual Seminar of the
Canadian Mathematical Congress, Queen's Papers in Pure and Applied
Mathematics, No. 48, Queen's University, Kingston, Ontario, 1978, pp.
487-495.
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- Representations of GL$_2(R)$ and GL$_2(C)$, Automorphic
Forms, Representations, and $L$-Functions, Proceedings of Symposia
in Pure Mathematics 33 (1979), Part 1, American Mathematical Society,
Providence, Rhode Island, pp. 87-91.
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- (with G. Zuckerman) Normalizing factors, tempered
representations, and $L$-groups, Automorphic Forms,
Representations, and $L$-Functions, Proceedings of Symposia in Pure
Mathematics 33 (1979), Part 1, American Mathematical Society,
Providence, Rhode Island, pp. 93-105.
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- (with E. M. Stein) Intertwining operators for semisimple groups
II, Inventiones Mathematicae 60 (1980), 9-84.
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- (with G. Zuckerman) Multiplicity one fails for $\frak p$-adic
unitary principal series, Hiroshima Mathematical Journal 10
(1980), 295-309.
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- Notes on covering spaces, duplicated notes, Cornell University,
Fall 1981.
Commentary |
Original notes
in PDF.
- (with S. S. Gelbart) Irreducible constituents of principal
series of SL$_n(k)$, Duke Mathematical Journal 48 (1981),
313-326.
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- (with E. M. Stein) Some new intertwining operators for
semisimple groups, Non Commutative Harmonic Analysis and Lie Groups,
Lecture Notes in Mathematics 880 (1981), Springer-Verlag, New York, pp.
303-336.
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- Letter to David Vogan, Langlands L-classes exist for SU(3,2) that
contain a mixture of unitary and nonunitary representations, October
19, 1982.
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- (with S. S. Gelbart) $L$-indistinguishability and $R$ groups for
the special linear group, Advances in Mathematics 43 (1982),
101-121.
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- (with B. Speh) Irreducible unitary representations of $SU(2,2)$,
Journal of Functional Analysis 45 (1982), 41-73.
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- (with B. Speh) Status of classification of irreducible unitary
representations, Harmonic Analysis, Lecture Notes in
Mathematics 908 (1982), Springer-Verlag, New York, pp. 1-38.
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- Commutativity of intertwining operators for semisimple groups,
Compositio Mathematica 46 (1982), 33-84.
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- (with G. J. Zuckerman) Classification of irreducible tempered
representations of semisimple groups, Annals of Mathematics
116 (1982), 389-501, and 119 (1984), 639.
Reprint of 1982 article:
PDF.
Reprint of 1984 typesetter's correction: PDF.
- Representation Theory of Semisimple Groups, by Examples,
preliminary edition, Université Paris VII, Paris, 1982.
- Minimal K-type formula, Non Commutative Harmonic Analysis
and Lie Groups, Lecture Notes in Mathematics 1020 (1983),
Springer-Verlag, New York, pp. 107-118.
Reprint in PDF.
Guide to details
of proof: HTML.
| First set of handwritten notes giving
proof: PDF. |
Second set of handwritten notes giving proof: PDF.
- (with B. Speh) The role of basic cases in classification:
Theorems about unitary representations applicable to SU(N,2), Non
Commutative Harmonic Analysis and Lie Groups, Lecture Notes in
Mathematics 1020 (1983), Springer-Verlag, New York, pp. 119-160.
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- Unitary representations and basic cases, Lie Group
Representations I, Lecture Notes in Mathematics 1024 (1983),
Springer-Verlag, New York, pp. 77-98.
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- Investigations of unitary representations of semisimple Lie
groups, Topics in Modern Harmonic Analysis I, Proceedings of a
Seminar Held in Torino and Milano May-June 1982, Istituto Nazionale
di Alta Matematica Francesco Severi, Rome, 1983, pp. 9-43.
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- (with M. W. Baldoni Silva) Indefinite intertwining operators,
Proceedings of the National Academy of Sciences of the USA 81
(1984), 1272-1275.
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- Langlands classification and unitary dual of $SU(2,2)$,
Applications of Group Theory in Physics and Mathematical Physics,
M. Flato, P. Sally, and G. Zuckerman (eds.), Lectures in Applied
Mathematics 21 (1985), American Mathematical Society, Providence, Rhode
Island, pp. 209-217.
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- Representation Theory of Semisimple Groups: An Overview
Based on Examples, Princeton Mathematical Series 36, Princeton
University Press, Princeton, New Jersey, 1986.
Access to the table of
contents, the preface, and a list of corrections.
- (with M. W. Baldoni-Silva) Unitary representations induced from
maximal parabolic subgroups, Journal of Functional Analysis
69 (1986), 21-120.
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- (with D. A. Vogan) Duality theorems in relative Lie
algebra cohomology, duplicated notes, SUNY Stony Brook and
Massachusetts Institute of Technology, 1986.
Commentary |
Original notes
in PDF.
- (with M. W. Baldoni-Silva) Indefinite intertwining operators II,
Analisi Armonica, Spazi Simmetrici e Teoria della Probabilità,
Cortona 2-5 Luglio 1984, Symposia Mathematica 29 (1987), Istituto
Nazionale di Alta Matematica Francesco Severi, Rome, pp. 1-44.
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in PDF.
- (with M. W. Baldoni-Silva) Irreducible unitary representations
of some groups of real rank two, Non-Commutative Harmonic Analysis
and Lie Groups, Lecture Notes in Mathematics 1243 (1987),
Springer-Verlag, New York, pp. 15-36.
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- (with M. W. Baldoni-Silva) Vogan's algorithm for computing
composition series, Non-Commutative Harmonic Analysis and Lie
Groups, Lecture Notes in Mathematics 1243 (1987), Springer-Verlag,
New York, pp. 37-72.
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PDF.
- Lie Groups, Lie Algebras, and Cohomology, Princeton
Mathematical Notes 34, Princeton University Press, Princeton, New
Jersey, 1988.
Access to the table of
contents, the preface, and a list of corrections.
- (with M. W. Baldoni-Silva) Intertwining operators and unitary
representations I, Journal of Functional Analysis 82 (1989),
151-236.
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- (with M. W. Baldoni-Silva) Intertwining operators and unitary
representations II, Société Mathématique de France, Astérisque
171-172 (1989), 131-162.
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- (with M. W. Baldoni-Silva) A construction of unitary
representations in parabolic rank two, Annali della Scuola Normale
Superiore di Pisa 16 (1989), 579-601.
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- CRM Summer School Course on Representations of Real
Reductive Groups, Publications CRM, Université de Montréal,
Montréal, 1990.
Access to the table of contents and
the preface.
- Imbedding discrete series in $L^2(G/H)$, in N. V. Pedersen
(ed.), Harmonic Analysis on Lie Groups (Sandbjerg Estate, August
26-30, 1991), Copenhagen University Mathematics Institute, Report
Series 1991, No. 3, Copenhagen, 1991, 27-29.
Reprint in PDF.
- (with M. W. Baldoni-Silva) Intertwining operators into
$L^2(G/H)$, Representation Theory of Lie Groups and Lie Algebras,
Fuji-Kawaguchiko, Aug 31-Sep 3, 1990, T. Kawazoe, T. Oshima, and S.
Sano (eds.), World Scientific, Singapore, 1992, pp. 95-119.
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- (with L. Barchini and R. Zierau) Intertwining operators into
Dolbeault cohomology representations, Journal of Functional
Analysis 107 (1992), 302-341.
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- Elliptic Curves, Princeton Mathematical Notes 40,
Princeton University Press, Princeton, New Jersey, 1992.
Access to the table of
contents, the preface, and lists of corrections. (This book grew
out of notes of a course in India by Don Zagier in 1998. To
download a copy of the notes, click
here.)
- Introduction to representations in analytic cohomology, The
Penrose Transform and Analytic Cohomology in Representation Theory,
M. Eastwood, J. Wolf, and R. Zierau (eds.), Contemporary Mathematics
154 (1993), American Mathematical Society, Providence, Rhode Island,
pp. 1-19.
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- Local Langlands correspondence: the archimedean case,
Motives, Proceedings of Symposia in Pure Mathematics 55 (1994),
Part 2, American Mathematical Society, Providence, Rhode Island, pp.
393-410.
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- (with D. A. Vogan) Cohomological Induction and Unitary
Representations, Princeton Mathematical Series 45, Princeton
University Press, Princeton, New Jersey, 1995.
Access to the table of contents, the
preface, and a list of corrections.
- Group representations and harmonic analysis from Euler to
Langlands, Part I, Notices of the American Mathematical Society
43 (1996), 410-415.
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- Group representations and harmonic analysis from Euler to
Langlands, Part II, Notices of the American Mathematical Society
43 (1996), 537-549.
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- Lie Groups Beyond an Introduction, Progress in
Mathematics 140, Birkhäuser, Boston, 1996. Reprinted with corrections,
2001.
Access to the corrected pages
appearing in the 2001 reprint.
- A quick proof of the classification of simple real Lie algebras,
Proceedings of the American Mathematical Society 124
(1996), 3257-3259.
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- Exceptional unitary representations of semisimple Lie groups,
Representation Theory 1 (1997), 1-24.
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- (editor with T. N. Bailey) Representation Theory and
Automorphic Forms; An Instructional Conference at the International
Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of
Symposia in Pure Mathematics 61 (1997), American Mathematical Society,
Providence, Rhode Island.
Access to the table of
contents and the foreword.
- Structure theory of semisimple Lie groups, Representation
Theory and Automorphic Forms; An Instructional Conference at the
International Centre for Mathematical Sciences, Edinburgh, 1996,
Proceedings of Symposia in Pure Mathematics 61 (1997), American
Mathematical Society, Providence, Rhode Island, pp. 1-27.
Reprint in PDF.
- Introduction to the Langlands program, Representation
Theory and Automorphic Forms; An Instructional Conference at the
International Centre for Mathematical Sciences, Edinburgh, 1996,
Proceedings of Symposia in Pure Mathematics61 (1997), American
Mathematical Society, Providence, Rhode Island, pp. 245-302.
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- Theoretical aspects of the trace formula for $GL(2)$,
Representation Theory and Automorphic Forms; An Instructional
Conference at the International Centre for Mathematical Sciences,
Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61
(1997), American Mathematical Society, Providence, Rhode Island, pp.
355-405.
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- (with J. D. Rogawski) Applications of the trace formula,
Representation Theory and Automorphic Forms; An Instructional
Conference at the International Centre for Mathematical Sciences,
Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61
(1997), American Mathematical Society, Providence, Rhode Island, pp.
413-431.
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- Survey of irreducible unitary representations of semisimple Lie
groups, GROUP21: Physical Applications and Mathematical Aspects of
Geometry, Groups, and Algebras, Proceedings of the XXI International
Colloquium, vol. 1, World Scientific, Singapore, 1997, pp. 89-98.
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- André Weil: A prologue, Notices of the American Mathematical
Society 46 (1999), 434-439.
Abstract | Reprint in PDF.
- Anneli Lax's Research Mathematics, Notices of the American
Mathematical Society 47 (2000), 768.
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- (with P. E. Trapa) Representations of semisimple Lie groups,
Representation Theory of Lie Groups , J. Adams and D. Vogan
(eds.), IAS/Park City Mathematics Series, vol. 8, American Mathematical
Society, Providence, 2000, pp. 5-87.
Reprint in PDF.
- Intertwining operators and small unitary representations,
The Mathematical Legacy of Harish-Chandra; An AMS Special Session
Honoring the Memory of Harish-Chandra, Baltimore, 1998,
Proceedings of Symposia in Pure Mathematics 68 (2000), American
Mathematical Society, Providence, Rhode Island, pp. 403-431.
Abstract | Reprint in PDF.
- Nomination for David A. Vogan Jr. as President Elect of the
American Mathematical Society, Notices of the American
Mathematical Society 48 (2001), 853-854.
Abstract | Reprint in PDF.
- Representation Theory of Semisimple Groups: An Overview Based
on Examples, paperback reprint of the original 1986 hardback
edition, Princeton Landmarks in Mathematics, Princeton University
Press, 2001. ISBN: 0-691-09089-0.
Access to the table of
contents, the two prefaces, and a list of corrections.
- Branching theorems for compact symmetric spaces,
Representation Theory 5 (2001), 404-436.
Abstract | Reprint in PDF.
- Lie Groups Beyond an Introduction, Second Edition,
Progress in Mathematics, Vol. 140, Birkhäuser, Boston, 2002. ISBN:
0-8176-4259-5.
Access to files of corrections,
the table of contents, the two prefaces, and abstracts of chapters new
or substantially changed from the first edition.
- The Gindikin-Karpelevic formula and intertwining operators,
Lie Groups and Symmetric Spaces, In Memory of F. I. Karpelevich,
American Mathematical Society Translations (2), 210 (2003), 145-159.
Reprint in PDF.
- Geometric interpretations of two branching theorems of D.E.
Littlewood, Journal of Algebra 270 (2003), 728-754.
Abstract | Reprint in PDF.
- Analytic continuation of nonholomorphic discrete series for
classical groups, Noncommutative Harmonic Analysis in Honor of
Jacques Carmona, Progress in Mathematics, Vol. 220, Birkhäuser,
Boston, 2004, pp. 253-289.
ISBN: 0-8176-3207-7.
Abstract | Reprint in PDF.
- Nilpotent orbits and some small unitary representations of
indefinite orthogonal groups, Journal of Functional Analysis
209 (2004), 36-100.
Abstract | Reprint in PDF.
- Salomon Bochner, August 20, 1899--May 2, 1982, Biographical
Memoirs 85 (2004), 40-61.
Reprint in PDF.
- ``Armand Borel (1923-2003),'' editor's note to article with eight
authors, Notices of the American Mathematical Society 51
(2004), 498-524; republished in Asian Journal of Mathematics
8,
No. 4 (2004), pp. xlvii-xlix.
Reprint of Notices article in
PDF | Reprint of editor's note from Asian Journal of
Mathematics in PDF.
- ``Weil's letter to his sister,'' letter to the editor,
Notices of the American Mathematical Society 52 (2005), 598-599.
Reprint in PDF.
- Basic Real Analysis, Cornerstones, Birkhäuser, Boston,
2005. ISBN: 0-8176-3250-6.
Access to files of front matter
and a of corrections.
- Advanced Real Analysis, Cornerstones, Birkhäuser, Boston,
2005. ISBN: 0-8176-4382-6.
Access to files of front matter
and a list of corrections.
- Basic Algebra, Cornerstones, Birkhäuser, Boston, 2006.
ISBN: 0-8176-3248-4.
Access to files of front matter
and a list of corrections.
- (with Henri Carayol) Limits of discrete series with infinitesimal
character zero, Transactions of the American Mathematical Society
359 (2007), 5611-5651.
Abstract | Reprint in PDF.
- Advanced Algebra, Cornerstones, Birkhäuser, Boston, 2007.
ISBN: 0-8176-4522-5.
Access to files of front matter
and a list of corrections.
- Prerequisites for the Langlands program, Automorphic Forms
and the Langlands Program, Advanced Lectures in Mathematics 9
(2009), International Press, Somerville, Massachusetts, pp. 1-9.
Abstract | Reprint in PDF.
- First steps with the Langlands program, Automorphic Forms
and the Langlands Program, Advanced Lectures in Mathematics 9
(2009), International Press, Somerville, Massachusetts, pp. 10-20.
Abstract | Reprint in PDF.
- Basic Real Analysis, digital second
edition, published by the author, 2016. No ISBN.
Access to download book.
- Advanced Real Analysis, digital second edition, published
by the author, 2016. No ISBN.
Access to download book.
- Basic Algebra, digital second edition, published by the
author, 2016. No ISBN.
Access to download book. Access to a list of corrections.
- Advanced Algebra, digital second edition, published by
the author, 2016. No ISBN.
Access to download book.
Book reviews
- Review of Lie Groups, Lie Algebras, and Their
Representations by V. S. Varadarajan and Compact Lie Groups
and Their Representations by D. P. Zhelobenko, Bulletin of
the American Mathematical Society 81 (1975), 865-872.
Reprint in PDF.
- Review of Unitary Representations of Reductive Lie Groups
by D. A. Vogan, Bulletin of the American Mathematical Society
(N.S.) 21 (1989), 380-384.
Reprint in PDF.
- Review of Matrix Groups: An Introduction to Lie Group Theory
by Andrew Baker and Lie Groups: An Introduction Through Linear
Groups by Wulf Rossmann, American Mathematical Monthly
110 (2003), 446-455.
Abstract | Reprint in PDF.
- Review of Love and Math: The Heart of Hidden Reality by
Edward Frenkel, Notices of the American Mathematical Society
61 (2014), 1056-1060.
Reprint in PDF.
Other writing
- (with P. Shaman) Certification of Algorithm 42, Invert,
Communications of the Association for Computing Machinery 4(11)
(1961), 498. Reprint in PDF.
- (with S. J. Garland) Algorithm 99, Evaluation of Jacobi symbol,
Communications of the Association for Computing Machinery 5(6)
(1962), 345-346. Reprint in PDF.
- Personal unofficial notes of a two-semester course
Functional Analysis given by William Feller, Princeton University,
Fall 1962 and Spring 1963. Scanned versions: PDF for Fall 1962, PDF for Spring 1963.
- (with A. Jackson) AMS in the Twentieth Century, Notices of
the American Mathematical Society, 1999-2000. Reprint in PDF.
- Founding of the Episcopal Church, All Souls Episcopal
Church, St. James, New York, 2007-08. Reprint in PDF.
Last modified: 1/13/2017