Symmetry Breaking for Representations of Rank One Orthogonal Groups. (Record no. 124856)
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| fixed length control field | 06340nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4832036 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131156.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2015 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470426156 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470419226 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4832036 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4832036 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11367321 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)920024642 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QC793.3.S9.K633 2015 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 12/.482 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Kobayashi, Toshiyuki. |
| 245 10 - TITLE STATEMENT | |
| Title | Symmetry Breaking for Representations of Rank One Orthogonal Groups. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2015. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2015. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (124 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.238 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Symmetry breaking for the spherical principal series representations -- 2.1. Notation and review of previous results -- 2.2. Finite-dimensional subquotients of disconnected groups -- 2.3. Symmetry breaking operators and spherical principal series representations -- 2.4. Multiplicities for composition factors -- Chapter 3. Symmetry breaking operators -- 3.1. Restriction of representations and symmetry breaking operators -- 3.2. Distribution kernels of symmetry breaking operators -- 3.3. Differential intertwining operators -- 3.4. Smooth representations and intertwining operators -- 3.5. Symmetry breaking operators for principal series representations -- 3.6. Meromorphic continuation of symmetry breaking operators -- Chapter 4. More about principal series representations -- 4.1. Models of principal series representations -- 4.2. Explicit -finite functions in the non-compact model -- 4.3. Normalized Knapp-Stein intertwining operator -- Chapter 5. Double coset decomposition '\ / -- Chapter 6. Differential equations satisfied by the distribution kernels of symmetry breaking operators -- 6.1. A system of differential equations for symmetry breaking operators -- 6.2. The solutions ℴ (ℝⁿ∖{0} -- , ) -- Chapter 7. -finite vectors and regular symmetry breaking operators ̃ _{ , } -- 7.1. Distribution kernel \ka{ } and its normalization -- 7.2. Preliminary results -- 7.3. Proof of Proposition 7.3 -- Chapter 8. Meromorphic continuation of regular symmetry breaking operators \ka{ } -- 8.1. Recurrence relations of the distribution kernels \ka{ } -- 8.2. Functional equations -- 8.3. 8.3 Support of \KA{ } -- 8.4. Renormalization \AAt_{ , } for ∈-ℕ -- Chapter 9. Singular symmetry breaking operator \B_{ , } -- 9.1. Singular symmetry breaking operator \B_{ , }. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 9.2. -finite vectors and singular operators \tB{ } -- 9.3. Proof of Theorem 9.1 -- 9.4. Support of the distribution kernel of \B_{ , } -- 9.5. Renormalization \BB_{ , } for \nulambda∈ _{ } with odd -- Chapter 10. Differential symmetry breaking operators -- 10.1. Power of the Laplacian -- 10.2. Juhl's family of differential operators -- 10.3. The kernel of the differential symmetry breaking operator \C_{ , } -- Chapter 11. Classification of symmetry breaking operators -- 11.1. Classification of symmetry breaking operators -- 11.2. Strategy of the proof of Theorem 11.1 -- 11.3. Lower bounds of the multiplicities -- 11.4. Extension of solutions from ℝⁿ∖{0} to ℝⁿ -- 11.5. Regular symmetry breaking operators -- 11.6. Singular symmetry breaking operators -- Chapter 12. Residue formulae and functional identities -- 12.1. Residues of symmetry breaking operators -- 12.2. Functional equations satisfied by singular symmetry breaking operators -- Chapter 13. Image of symmetry breaking operators -- 13.1. Finite-dimensional image for ∈-ℕ -- 13.2. Image for ∈ +ℕ -- 13.3. Spherical vectors and symmetry breaking operators -- Chapter 14. Application to analysis on anti-de Sitter space -- 14.1. Harmonic analysis on Lorentzian hyperbolic spaces -- 14.2. Application of symmetry breaking operators to anti-de Sitter spaces -- 14.3. Analysis on vector bundles over anti-de Sitter spaces -- Chapter 15. Application to branching laws of complementary series -- 15.1. Discrete spectrum in complementary series -- 15.2. ²-model of complementary series representations -- Chapter 16. Appendix -- 16.1. Gegenbauer polynomials -- 16.2. -Bessel function and its renormalization -- 16.3. Zuckerman derived functor modules _{ }( ) -- Acknowledgments -- References -- List of Symbols -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp--Stein intertwining operators of G and G' satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of G and G'. Some applications are included. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Broken symmetry (Physics). |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Speh, Birgit. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Kobayashi, Toshiyuki |
| Title | Symmetry Breaking for Representations of Rank One Orthogonal Groups |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2015 |
| International Standard Book Number | 9781470419226 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832036">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832036</a> |
| Public note | Click to View |
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