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008 240724s2011 xx o ||||0 eng d
020 _a9781470406172
_q(electronic bk.)
020 _z9780821847572
035 _a(MiAaPQ)EBC3114223
035 _a(Au-PeEL)EBL3114223
035 _a(CaPaEBR)ebr11039842
035 _a(OCoLC)922981771
040 _aMiAaPQ
_beng
_erda
_epn
_cMiAaPQ
_dMiAaPQ
050 4 _aQA387 -- .K633 2011eb
082 0 _a512/.582
100 1 _aKobayashi, Toshiyuki.
245 1 0 _aSchrödinger Model for the Minimal Representation of the Indefinite Orthogonal Group O(p,q).
250 _a1st ed.
264 1 _aProvidence :
_bAmerican Mathematical Society,
_c2011.
264 4 _c©2011.
300 _a1 online resource (145 pages)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aMemoirs of the American Mathematical Society ;
_vv.213
505 0 _aIntro -- Contents -- Chapter 1. Introduction -- 1.1. Differential operators on the isotropic cone -- 1.2. `Fourier transform' FC on the isotropic cone C -- 1.3. Kernel of FC and Bessel distributions -- 1.4. Perspectives from representation theory - finding smallest objects -- 1.5. Minimal representations of simple Lie groups -- 1.6. Schrödinger model for the Weil representation -- 1.7. Schrödinger model for the minimal representation of O(p,q) -- 1.8. Uncertainty relation - inner products and G-actions -- 1.9. Special functions and minimal representations -- 1.10. Organization of this book -- 1.11. Acknowledgements -- Chapter 2. Two models of the minimal representation of O(p,q) -- 2.1. Conformal model -- 2.2. L2-model (the Schrödinger model) -- 2.3. Lie algebra action on L2(C) -- 2.4. Commuting differential operators on C -- 2.5. The unitary inversion operator FC=(w0) -- Chapter 3. K-finite eigenvectors in the Schrödinger model L2(C) -- 3.1. Result of this chapter -- 3.2. K Mmax-invariant subspaces Hl,k -- 3.3. Integral formula for the K Mmax-intertwiner -- 3.4. K-finite vectors fl,k in L2(C) -- 3.5. Proof of Theorem 3.1.1 -- Chapter 4. Radial part of the inversion -- 4.1. Result of this chapter -- 4.2. Proof of Theorem 4.1.1 (1) -- 4.3. Preliminary results on multiplier operators -- 4.4. Reduction to Fourier analysis -- 4.5. Kernel function Kl,k -- 4.6. Proof of Theorem 4.1.1 (2) -- Chapter 5. Main theorem -- 5.1. Result of this chapter -- 5.2. Radon transform for the isotropic cone C -- 5.3. Spectra of K'-invariant operators on Sp-2Sq-2 -- 5.4. Proof of Theorem 5.1.1 -- 5.5. Proof of Lemma 5.4.2 (Hermitian case q=2) -- 5.6. Proof of Lemma 5.4.2 (p,q&gt -- 2) -- Chapter 6. Bessel distributions -- 6.1. Meijer's G-distributions -- 6.2. Integral expression of Bessel distributions -- 6.3. Differential equations for Bessel distributions.
505 8 _aChapter 7. Appendix: special functions -- 7.1. Riesz distribution x+ -- 7.2. Bessel functions J, I, K, Y -- 7.3. Associated Legendre functions P -- 7.4. Gegenbauer polynomials Cl -- 7.5. Spherical harmonics Hj(Rm) and branching laws -- 7.6. Meijer's G-functions Gp,qm,n(to1.5. x |to1.5. a1, @let@token , ap b1, @let@token , bq)to1.5. -- 7.7. Appell's hypergeometric functions F1, F2, F3, F4 -- 7.8. Hankel transform with trigonometric parameters -- 7.9. Fractional integral of two variables -- Bibliography -- List of Symbols -- Index.
588 _aDescription based on publisher supplied metadata and other sources.
590 _aElectronic 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 _aRepresentations of Lie groups.
650 0 _aSchrödinger equation.
655 4 _aElectronic books.
700 1 _aMano, Gen.
776 0 8 _iPrint version:
_aKobayashi, Toshiyuki
_tSchrödinger Model for the Minimal Representation of the Indefinite Orthogonal Group O(p,q)
_dProvidence : American Mathematical Society,c2011
_z9780821847572
797 2 _aProQuest (Firm)
830 0 _aMemoirs of the American Mathematical Society
856 4 0 _uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114223
_zClick to View
999 _c69754
_d69754