The heat kernel and theta inversion on SL (C)
The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one ma...
Shranjeno v:
| Auteurs principaux: | , |
|---|---|
| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Izdaja: | 1st ed. 2008. |
| Serija: | Springer Monographs in Mathematics
|
| Teme: | |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
L'impression du document génère 308 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The heat kernel and theta inversion on SL (C), Jay Jorgenson, Serge Lang, 2008, New York, Springer, 1 vol. (X-319 p.), Springer Monographs in Mathematics, 0-387-38031-0 • The Heat Kernel and Theta Inversion on SL2(C), Texte imprimé, 9780387564050 • The Heat Kernel and Theta Inversion on SL2(C), Texte imprimé, 9781441922823 |
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| 008 | 090420q2000 xxe ||| |||| 00| 0 eng d | ||
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| 041 | 0 | |a eng | |
| 082 | |a 512.7 | ||
| 084 | |a 11M36. 2010 | ||
| 084 | |a 11F72. 2010 | ||
| 084 | |a 58J35. 2010 | ||
| 100 | 1 | |a Jorgenson, Jay, |d 1963- | |
| 245 | 1 | 0 | |a The heat kernel and theta inversion on SL (C) |c Jay Jorgenson, Serge Lang. |
| 250 | |a 1st ed. 2008. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 2196-9922 | |
| 500 | |a L'impression du document génère 308 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 0 | |a Gaussians, Spherical Inversion, and the Heat Kernel -- Spherical Inversion on SL2(C) -- The Heat Gaussian and Heat Kernel -- QED, LEG, Transpose, and Casimir -- Enter ?: The General Trace Formula -- Convergence and Divergence of the Selberg Trace -- The Cuspidal and Noncuspidal Traces -- The Heat Kernel on ?\G/K -- The Fundamental Domain -- ?-Periodization of the Heat Kernel -- Heat Kernel Convolution on (?\G/K) -- Fourier-Eisenstein Eigenfunction Expansions -- The Tube Domain for ?? -- The ?/U-Fourier Expansion of Eisenstein Series -- Adjointness Formula and the ?\G-Eigenfunction Expansion -- The Eisenstein-Cuspidal Affair -- The Eisenstein Y-Asymptotics -- The Cuspidal Trace Y-Asymptotics -- Analytic Evaluations | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of SL2(Z[i]) acting on SL2(C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations | ||
| 650 | |a Fonctions thêta | ||
| 650 | |a Formules de trace | ||
| 650 | |a Noyaux (analyse fonctionnelle) | ||
| 650 | |a Équation de la chaleur | ||
| 650 | |a Inversions (géométrie) | ||
| 700 | 1 | |a Lang, Serge, |d 1927-2005. |4 aut | |
| 776 | 0 | |0 12910342X |t The heat kernel and theta inversion on SL (C) |f Jay Jorgenson, Serge Lang |d 2008 |c New York |n Springer |p 1 vol. (X-319 p.) |s Springer Monographs in Mathematics |z 0-387-38031-0 | |
| 776 | 0 | |t The Heat Kernel and Theta Inversion on SL2(C) |b Texte imprimé |z 9780387564050 | |
| 776 | 0 | |t The Heat Kernel and Theta Inversion on SL2(C) |b Texte imprimé |z 9781441922823 | |
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