Publications by Anthony W. Knapp



Below is a list of my publications---books, articles, and other writing. In some cases links are provided to places on the web where an abstract or reprint of the article may be found.

Skip to: 1964 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 | 2010 | Book reviews | Other writing.


Books and articles
  1. Distal functions, Proceedings of the National Academy of Sciences of the USA 52 (1964), 1409-1412.
    Reprint in PDF.

  2. Connection between Brownian motion and potential theory, Journal of Mathematical Analysis and Applications 12 (1965), 328-349.
    Reprint in PDF.

  3. Regular boundary points in Markov chains, Proceedings of the American Mathematical Society 17 (1966), 435-440.
    Reprint in PDF.

  4. (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.

  5. Decomposition theorem for bounded uniformly continuous functions on a group, American Journal of Mathematics 88 (1966), 902-914.
    Reprint in PDF.

  6. Distal functions on groups, Transactions of the American Mathematical Society 128 (1967), 1-40.
    Reprint in PDF.

  7. Fatou's theorem for symmetric spaces I, Annals of Mathematics 88 (1968), 106-127.
    Reprint in PDF.

  8. Doubly generated Fuchsian groups, Michigan Mathematical Journal 15 (1968), 289-304.
    Reprint in PDF.

  9. 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.
    Reprint in PDF.

  10. (with P. J. Kahn) Equivariant maps onto minimal flows, Mathematics Systems Theory 2 (1968), 319-324.
    Reprint in PDF.

  11. (with E. M. Stein) Singular integrals and the principal series, Proceedings of the National Academy of Sciences of the USA 63 (1969), 281-284.
    Reprint in PDF.

  12. (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.
    Reprint in PDF.

  13. (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.
    Reprint in PDF.

  14. (with E. M. Stein) Intertwining operators for semisimple groups, Annals of Mathematics 93 (1971), 489-578.
    Reprint in PDF.

  15. (with R. E. Williamson) Poisson integrals and semisimple groups, Journal d'Analyse Mathématique 24 (1971), 53-76.
    Reprint in PDF.

  16. (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.
    Reprint in PDF.

  17. 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.
    Reprint in PDF.

  18. (with K. Okamoto) Limits of holomorphic discrete series, Journal of Functional Analysis 9 (1972), 375-409.
    Reprint in PDF.

  19. 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.
    Reprint in PDF.

  20. Commutativity of intertwining operators, Bulletin of the American Mathematical Society 79 (1973), 1016-1018.
    Reprint in PDF.

  21. (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.

  22. (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.
    Reprint in PDF.

  23. A Szegö kernel for discrete series, Proceedings of the International Congress of Mathematicians, 1974, 2 (1975), Canadian Mathematical Congress, 99-104.
    Reprint in PDF.

  24. Weyl group of a cuspidal parabolic, Annales Scientifiques de l'Ecole Normale Supérieure 8 (1975), 275-294.
    Reprint in PDF.

  25. (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.
    Reprint in PDF.

  26. Commutativity of intertwining operators II, Bulletin of the American Mathematical Society 82 (1976), 271-273.
    Reprint in PDF.

  27. (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.

  28. (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.
    Reprint in PDF.

  29. (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.

  30. (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.
    Reprint in PDF.

  31. (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.
    Reprint in PDF.

  32. 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.

  33. 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.
    Reprint in PDF.

  34. (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.
    Reprint in PDF.

  35. (with E. M. Stein) Intertwining operators for semisimple groups II, Inventiones Mathematicae 60 (1980), 9-84.
    Reprint in PDF.

  36. (with G. Zuckerman) Multiplicity one fails for $\frak p$-adic unitary principal series, Hiroshima Mathematical Journal 10 (1980), 295-309.
    Reprint in PDF.

  37. (with S. S. Gelbart) Irreducible constituents of principal series of SL$_n(k)$, Duke Mathematical Journal 48 (1981), 313-326.
    Reprint in PDF.

  38. (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.
    Reprint in PDF.

  39. Letter to David Vogan, Langlands L-classes exist for SU(3,2) that contain a mixture of unitary and nonunitary representations, October 19, 1982.
    Reprint in PDF.

  40. (with S. S. Gelbart) $L$-indistinguishability and $R$ groups for the special linear group, Advances in Mathematics 43 (1982), 101-121.
    Reprint in PDF.

  41. (with B. Speh) Irreducible unitary representations of $SU(2,2)$, Journal of Functional Analysis 45 (1982), 41-73.
    Reprint in PDF.

  42. (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.
    Reprint in PDF.

  43. Commutativity of intertwining operators for semisimple groups, Compositio Mathematica 46 (1982), 33-84.
    Reprint in PDF.

  44. (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.

  45. Representation Theory of Semisimple Groups, by Examples, preliminary edition, Université Paris VII, Paris, 1982.

  46. 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.

  47. (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.
    Reprint in PDF.

  48. Unitary representations and basic cases, Lie Group Representations I, Lecture Notes in Mathematics 1024 (1983), Springer-Verlag, New York, pp. 77-98.
    Reprint in PDF.

  49. 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.
    Reprint in PDF.

  50. (with M. W. Baldoni Silva) Indefinite intertwining operators, Proceedings of the National Academy of Sciences of the USA 81 (1984), 1272-1275.
    Reprint in PDF.

  51. 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.
    Reprint in PDF.

  52. 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.

  53. (with M. W. Baldoni-Silva) Unitary representations induced from maximal parabolic subgroups, Journal of Functional Analysis 69 (1986), 21-120.
    Reprint in PDF.

  54. (with D. A. Vogan) Duality theorems in relative Lie algebra cohomology, duplicated notes, SUNY Stony Brook and Massachusetts Institute of Technology, 1986.

  55. (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.
    Reprint in PDF.

  56. (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.
    Reprint in PDF.

  57. (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.
    Reprint in PDF.

  58. 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.

  59. (with M. W. Baldoni-Silva) Intertwining operators and unitary representations I, Journal of Functional Analysis 82 (1989), 151-236.
    Reprint in PDF.

  60. (with M. W. Baldoni-Silva) Intertwining operators and unitary representations II, Société Mathématique de France, Astérisque 171-172 (1989), 131-162.
    Reprint in PDF.

  61. (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.
    Reprint in PDF.

  62. 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.

  63. 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.

  64. (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.
    Reprint in PDF.

  65. (with L. Barchini and R. Zierau) Intertwining operators into Dolbeault cohomology representations, Journal of Functional Analysis 107 (1992), 302-341.
    Reprint in PDF.

  66. 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.

  67. 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.
    Reprint in PDF.

  68. 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.
    Reprint in PDF.

  69. (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.

  70. Group representations and harmonic analysis from Euler to Langlands, Part I, Notices of the American Mathematical Society 43 (1996), 410-415.
    Reprint in PDF.

  71. Group representations and harmonic analysis from Euler to Langlands, Part II, Notices of the American Mathematical Society 43 (1996), 537-549.
    Reprint in PDF.

  72. 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.

  73. A quick proof of the classification of simple real Lie algebras, Proceedings of the American Mathematical Society 124 (1996), 3257-3259.
    Reprint in PDF.

  74. Exceptional unitary representations of semisimple Lie groups, Representation Theory 1 (1997), 1-24.
    Reprint in PDF.

  75. (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.

  76. 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.

  77. 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.
    Reprint in PDF.

  78. 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.
    Reprint in PDF.

  79. (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.
    Reprint in PDF.

  80. 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.
    Reprint in PDF.

  81. André Weil: A prologue, Notices of the American Mathematical Society 46 (1999), 434-439.
    Abstract | Reprint in PDF.

  82. Anneli Lax's Research Mathematics, Notices of the American Mathematical Society 47 (2000), 768.
    Reprint in PDF.

  83. (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.

  84. 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.
    Reprint in PDF.
    Abstract.

  85. 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.

  86. 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.

  87. Branching theorems for compact symmetric spaces, Representation Theory 5 (2001), 404-436.
    Abstract | Reprint in PDF.

  88. 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.

  89. 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.

  90. Geometric interpretations of two branching theorems of D.E. Littlewood, Journal of Algebra 270 (2003), 728-754.
    Abstract | Reprint in PDF.

  91. 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.

  92. Nilpotent orbits and some small unitary representations of indefinite orthogonal groups, Journal of Functional Analysis 209 (2004), 36-100.
    Abstract | Reprint in PDF.

  93. Salomon Bochner, August 20, 1899--May 2, 1982, Biographical Memoirs 85 (2004), 40-61.
    Reprint in PDF.

  94. ``Armand Borel (1923-2003),'' editor's note to article with eight authors, Notices of the American Mathematical Society 51 (2004), 500; republished in Asian Journal of Mathematics 8, No. 4 (2004), pp. xlvii-xlix.
    Reprint of Notices page in PDF.

  95. ``Weil's letter to his sister,'' letter to the editor, Notices of the American Mathematical Society 52 (2005), 598-599.
    Reprint in PDF.

  96. Basic Real Analysis, Cornerstones, Birkhäuser, Boston, 2005. ISBN: 0-8176-3250-6.
    Access to files of front matter, sample pages from three chapters, and a list of corrections.

  97. Advanced Real Analysis, Cornerstones, Birkhäuser, Boston, 2005. ISBN: 0-8176-4382-6.
    Access to files of front matter, sample pages from four chapters, and a short list of corrections.

  98. Basic Algebra, Cornerstones, Birkhäuser, Boston, 2006. ISBN: 0-8176-3248-4.
    Access to files of front matter, sample pages from five chapters, and a short list of corrections.

  99. (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.

  100. Advanced Algebra, Cornerstones, Birkhäuser, Boston, 2007. ISBN: 0-8176-4522-5.
    Access to files of front matter and to sample pages from five chapters.

  101. 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.

  102. 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.

  103. Basic Real Analysis, digital second edition, published by the author, 2016.  No ISBN.
    Access to download book.

  104. Advanced Real Analysis, digital second edition, published by the author, 2016.  No ISBN.
    Access to download book.

  105. Basic Algebra, digital second edition, published by the author, 2016.  No ISBN.
    Access to download book.  Access to a list of corrections.

  106. Advanced Algebra, digital second edition, published by the author, 2016.  No ISBN.
    Access to download book.


Book reviews
  1. 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.

  2. 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.

  3. 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.

  4. 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
  1. (with P. Shaman) Certification of Algorithm 42, Invert, Communications of the Association for Computing Machinery 4(11) (1961), 498. Reprint in PDF.

  2. (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.

  3. 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.

  4. (with A. Jackson) AMS in the Twentieth Century, Notices of the American Mathematical Society, 1999-2000. Reprint in PDF.

  5. Founding of the Episcopal Church, All Souls Episcopal Church, St. James, New York, 2007-08. Reprint in PDF.



Last modified: 8/25/2016