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Lectures on the spectrum of L [Gamma]

Lectures on the spectrum of L [Gamma]

Material type
단행본
Personal Author
Williams, Floyd L.
Title Statement
Lectures on the spectrum of L [Gamma] / Floyd L. Williams.
Publication, Distribution, etc
Harlow, Essex, England :   Longman Scientific & Technical ;   New York :   Wiley ,   1991.  
Physical Medium
348 p. ; 25 cm.
Series Statement
Pitman research notes in mathematics series , 0269-3674 ; 242
ISBN
047021757X (USA) 0582068630
Bibliography, Etc. Note
Includes bibliographical references (p. 338-348).
Subject Added Entry-Topical Term
Selberg trace formula. Spectral theory (Mathematics) Lie algebras.
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008 900917s1991 enk b 00010 eng
010 ▼a 90013548
020 ▼a 047021757X (USA)
020 ▼a 0582068630
035 ▼a 90013548
040 ▼a DLC ▼c DLC ▼d DLC
050 0 0 ▼a QA252.3 ▼b .W55 1990
082 0 0 ▼a 512/.55 ▼2 20
090 ▼a 512.55 ▼b W723L
093 ▼l 111023606
100 1 0 ▼a Williams, Floyd L.
245 1 0 ▼a Lectures on the spectrum of L [Gamma] / ▼c Floyd L. Williams.
260 0 ▼a Harlow, Essex, England : ▼b Longman Scientific & Technical ; ▼a New York : ▼b Wiley , ▼c 1991.
300 ▼a 348 p. ; ▼c 25 cm.
440 0 0 ▼a Pitman research notes in mathematics series , ▼x 0269-3674 ; ▼v 242
504 ▼a Includes bibliographical references (p. 338-348).
650 0 ▼a Selberg trace formula.
650 0 ▼a Spectral theory (Mathematics)
650 0 ▼a Lie algebras.

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No. 1 Location Main Library/Western Books/ Call Number 512.55 W723L Accession No. 111023606 Availability Available Due Date Make a Reservation Service B M
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No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 512.55 W723L Accession No. 111023606 Availability Available Due Date Make a Reservation Service B M
No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Sejong Academic Information Center/Science & Technology/ Call Number 512.55 W723L Accession No. 151004091 Availability Available Due Date Make a Reservation Service M
No. 2 Location Sejong Academic Information Center/Science & Technology/ Call Number 512.55 W723L Accession No. 452082103 Availability Available Due Date Make a Reservation Service M

Contents information

Table of Contents

CONTENTS
Preface
Introduction
Part I
  1. Measures on homogeneous spaces = 1
    Appendix 1. Surjectivity of Cc (G) → Cc (H\G) = 15
    Appendix 2. Surjectivity of Cc (A\G) → Cc (A\G/B) = 17
  2. The spectral theorem for a family of compact operators = 19
  3. Applications of Theorem 2.7 to certain unitary representations = 27
  4. The decomposition of L2 ( Γ \G) = 32
  5. The Selberg trace formula for compact quotients = 38
  6. Spinor spaces and spin modules = 45
    Appendix 1. More on the spin group = 66
Part II
  7. Discrete series multiplicities = 74
    Appendix 1. Harish-Chandra's theorem on the discrete series = 99
    Appendix 2. The holomorphic discrete series of SL(2,R) = 100
    Appendix 3. Dirac operators on homogeneous vector bundles over G/K = 103
    Appendix 4. Langlands' technical assumption on Γ = 108
  8. Cohomo1ogica1 interpretation of derived functor module multiplicities = 110
    Appendix 1. Action of the center of U(g) on Rq j W = 138
    Appendix 2. The discrete series as a derived functor module = 143
  9. Class 1 representations and spherical functions = 148
    Appendix 1. Commutativity of C4 (G) = 167
    Appendix 2. Iwasawa decomposition and Harish-Chandra c-function for SL(2,R) = 168
    Appendix 3. Spherical functions on SL(2,R) = 170
  10. The Matsushima-Murakami formula revisited = 176
  11. The Selberg trace formula in the rank 1 case = 179
    Appendix 1. Ix ( φ ) for x elliptic = 200
    Appendix 2. The trace formula for SL(2,R) = 208
  12. The Class 1 spectrum of Γ \G/K = 214
    Appendix 1. Solution of z'/z= ψ = 232
  13. The theta transform and its adjoint = 235
    Appendix 1. Computation of the measure dn ∞ for SL(2,R) = 259
    Appendix 2. Inversion formula for the Mellin transform = 261
  14. The Poisson summation formula = 265
    Appendix 1. A lemma involving the divisor function σν = 274
  15. Eisenstein series for SL(2,R), SL(2,Z) = 278
  16. The spectrum of L2 ( Γ \G/K) = 290
    Appendix 1. Two trivial observations = 315
  17. H u ·· ber's formula = 318
  18. Cohomological interpretation of limits of discrete series multiplicities = 331
References = 338

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