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- catalog abstract ""Harish-Chandra's general Plancherel inversion theorem admits a much shorter presentation for spherical functions. The authors have taken into account contributions by Helgason, Gangolli, Rosenberg, and Anker from the mid-1960s to 1990. Anker's simplification of spherical inversion on the Harish-Chandra Schwartz space had not yet made it into a book exposition. Previous expositions have a dealt with a general, wide class of Lie groups. This has made access to the subject difficult for outsiders, who may wish to connect some aspects with several if not all other parts of mathematics, and do so for specific cases of intrinsic interest. The essential features of Harish-Chandra theory are exhibited on SL[subscript n](R), but hundreds pages of background can be replaced by short direct verifications. The material becomes accessible to graduate students with essentially no background in Lie groups and representation theory. Spherical inversion is sufficient to deal with the heat kernel, which is at the center of the authors' current research. The book will serve as a self-contained background for parts of this research."--Jacket.".
- catalog contributor b12165222.
- catalog contributor b12165223.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description ""Harish-Chandra's general Plancherel inversion theorem admits a much shorter presentation for spherical functions. The authors have taken into account contributions by Helgason, Gangolli, Rosenberg, and Anker from the mid-1960s to 1990. Anker's simplification of spherical inversion on the Harish-Chandra Schwartz space had not yet made it into a book exposition. Previous expositions have a dealt with a general, wide class of Lie groups. This has made access to the subject difficult for outsiders, who may wish to connect some aspects with several if not all other parts of mathematics, and do so for specific cases of intrinsic interest.".
- catalog description "Ch. I. Iwasawa Decomposition and Positivity -- Ch. II. Invariant Differential Operators and the Iwasawa Direct Image -- Ch. III. Characters, Eigenfunctions, Spherical Kernel and W-Invariance -- Ch. IV. Convolutions, Spherical Functions and the Mellin Transform -- Ch. V. Gelfand -- Naimark Decomposition and the Harish-Chandra c-Function -- Ch. VI. Polar Decomposition -- Ch. VII. The Casimir Operator -- Ch. VIII. The Harish-Chandra Series and Spherical Inversion -- Ch. IX. General Inversion Theorems -- Ch. X. The Harish-Chandra Schwartz Space (HCS) and Anker's Proof of Inversion -- Ch. XI. Tube Domains and the L[superscript 1](Even L[superscript P]) HCS Spaces -- Ch. XII. SL[subscript n] (C).".
- catalog description "Includes bibliographical references (p. 411-421) and index.".
- catalog description "The essential features of Harish-Chandra theory are exhibited on SL[subscript n](R), but hundreds pages of background can be replaced by short direct verifications. The material becomes accessible to graduate students with essentially no background in Lie groups and representation theory. Spherical inversion is sufficient to deal with the heat kernel, which is at the center of the authors' current research. The book will serve as a self-contained background for parts of this research."--Jacket.".
- catalog extent "xx, 426 p. ;".
- catalog identifier "0387951156 (alk. paper)".
- catalog isPartOf "Springer monographs in mathematics".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "515/.53 21".
- catalog subject "Decomposition (Mathematics)".
- catalog subject "QA406 .J67 2001".
- catalog subject "Spherical functions.".
- catalog tableOfContents "Ch. I. Iwasawa Decomposition and Positivity -- Ch. II. Invariant Differential Operators and the Iwasawa Direct Image -- Ch. III. Characters, Eigenfunctions, Spherical Kernel and W-Invariance -- Ch. IV. Convolutions, Spherical Functions and the Mellin Transform -- Ch. V. Gelfand -- Naimark Decomposition and the Harish-Chandra c-Function -- Ch. VI. Polar Decomposition -- Ch. VII. The Casimir Operator -- Ch. VIII. The Harish-Chandra Series and Spherical Inversion -- Ch. IX. General Inversion Theorems -- Ch. X. The Harish-Chandra Schwartz Space (HCS) and Anker's Proof of Inversion -- Ch. XI. Tube Domains and the L[superscript 1](Even L[superscript P]) HCS Spaces -- Ch. XII. SL[subscript n] (C).".
- catalog title "Spherical inversion on SLn(R) / Jay Jorgenson, Serge Lang.".
- catalog type "text".