Articoli correlati a SL2(R): 105
Sinossi
SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.
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Contenuti
I General Results.- 1 The representation on Cc(G).- 2 A criterion for complete reducibility.- 3 L2 kernels and operators.- 4 Plancherel measures.- II Compact Groups.- 1 Decomposition over K for SL2(R).- 2 Compact groups in general.- III Induced Representations.- 1 Integration on coset spaces.- 2 Induced representations.- 3 Associated spherical functions.- 4 The kernel defining the induced representation.- IV Spherical Functions.- 1 Bi-invariance.- 2 Irreducibility.- 3 The spherical property.- 4 Connection with unitary representations.- 5 Positive definite functions.- V The Spherical Transform.- 1 Integral formulas.- 2 The Harish transform.- 3 The Mellin transfor.- 4 The spherical transform.- 5 Explicit formulas and asymptotic expansions.- VI The Derived Representation on the Lie Algebra.- 1 The derived representation.- 2 The derived representation decomposed over K.- 3 Unitarization of a representation.- 4 The Lie derivatives on G.- 5 Irreducible components of the induced representations.- 6 Classification of all unitary irreducible representations.- 7 Separation by the trace.- VII Traces.- 1 Operators of trace class.- 2 Integral formulas.- 3 The trace in the induced representation.- 4 The trace in the discrete series.- 5 Relation between the Harish transforms on A and K.- Appendix. General facts about traces.- VIII The PlanchereS Formula.- 1 Calculus lemma.- 2 The Harish transforms discontinuities.- 3 Some lemmas.- 4 The Plancherel formula.- IX Discrete Series.- 1 Discrete series in L2(G).- 2 Representation in the upper half plane.- 3 Representation on the disc.- 4 The lifting of weight m.- 5 The holomorphic property.- X Partial Differential Operators.- 1 The universal enveloping algebra.- 2 Analytic vectors.- 3 Eigenfunctions of ?f.- XI The Well Representation.- 1 1.- 4 Symmetry of the Laplace operator on ?\?.- 5 The Laplace operator on ?\?.- 6 Green’s functions and the Whittaker equation.- 7 Decomposition of the resolvant on ?\? for ? > 3/2.- 8 The equation $$ - \psi ''(y) = {\text{ }}\frac{{s(1 - s)}}{{{y^2}}}\psi (y)\;on\;\left[ {a,\infty } \right) $$.- 9 Eigenfunctions of the Laplacian in L2?\? = H.- 10 The resolvant equations for 0 < ? < 2.- 11 The kernel of the resolvant for 0 < ? < 2.- 12 The Eisenstein operator and Eisenstein functions.- 13 The continuous part of the spectrum.- 14 Several cusps.- Appendix 1 Bounded Hermitian Operators and Schur’s Lemma.- 1 Continuous functions of operators.- 2 Projection functions of operators.- Appendix 2 Unbounded Operators.- 1 Self-adjoint operators.- 2 The spectral measure.- 3 The resolvant formula.- Appendix 3 Meromorphic Families of Operators.- 1 Compact operators.- 2 Bounded operators.- Appendix 4 Elliptic PDF.- 1 Sobolev spaces.- 2 Ordinary estimates.- 3 Elliptic estimates.- 4 Compactness and regularity on the torus.- 5 Regularity in Euclidean space.- Appendix 5 Weak and Strong Analyticity.- 1 Complex theorem.- 2 Real theorem.- Symbols Frequently Used.
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Book by Lang S
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Edizione Internazionale
Sl2 (R)
Editore:
Secaucus, New Jersey, U.S.A.: Springer Verlag, 1985
ISBN 10: 0387961984
ISBN 13: 9780387961989
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Soft cover
Da: Sizzler Texts, SAN GABRIEL, CA, U.S.A.
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Soft cover. Condizione: New. Condizione sovraccoperta: New. International Edition. **International edition** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Codice articolo ABE-8206581452
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Edizione Internazionale
Sl2 (R)
Editore:
Springer, New York, NY, 1985
ISBN 10: 0387961984
ISBN 13: 9780387961989
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Trade paperback
Da: Aideo Books, San Marino, CA, U.S.A.
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Trade paperback. Condizione: New in new dust jacket. First edition. INTERNATIONAL EDITION. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Sewn binding. Cloth over boards. 428 p. Contains: Illustrations. Lecture Notes in Statistics, 105. Audience: General/trade. Codice articolo K3160000087
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