Quantization and Arithmetic
(12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. Consider on the line the distributions m (12) ? d (x)= ? (m)? x? , even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2 m?Z 2 i?x UnderaFouriertransformation,oru...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
Basel :
Birkhäuser Basel
2008.
Cham : Springer Nature |
| سلاسل: | Pseudo-Differential Operators, Theory and Applications
1 |
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Quantization and Arithmetic, Texte imprimé, 9783764398378 • Quantization and arithmetic, André Unterberger, Basel, Birkhäuser, 2008, 1 vol. (147 p.), Pseudo-Differential Operators, 978-3-7643-8790-7 |
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| 100 | 1 | |a Unterberger, André, |d 1940-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Quantization and Arithmetic |c André Unterberger. |
| 260 | |a Basel : |b Birkhäuser Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c 2008. | ||
| 490 | 0 | |a Pseudo-Differential Operators, Theory and Applications |v 1 |x 2297-0363 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a Weyl Calculus and Arithmetic -- Quantization -- Quantization and Modular Forms -- Back to the Weyl Calculus. | |
| 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. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a (12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. Consider on the line the distributions m (12) ? d (x)= ? (m)? x? , even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2 m?Z 2 i?x UnderaFouriertransformation,orundermultiplicationbythefunctionx ? e , the?rst(resp. second)ofthesedistributionsonlyundergoesmultiplicationbysome 24th (resp. 8th) root of unity. Then, consider the metaplectic representation Met, 2 a unitary representation in L (R) of the metaplectic group G, the twofold cover of the group G = SL(2,R), the de?nition of which will be recalled in Section 2: it extends as a representation in the spaceS (R) of tempered distributions. From what has just been said, if g is a point of G lying above g? G,andif d = d even g ?1 or d , the distribution d =Met(g )d only depends on the class of g in the odd homogeneousspace?\G=SL(2,Z)\G,uptomultiplicationbysomephasefactor, by which we mean any complex number of absolute value 1 depending only on g . On the other hand, a function u?S(R) is perfectly characterized by its scalar g productsagainstthedistributionsd ,sinceonehasforsomeappropriateconstants C , C the identities 0 1 g 2 2 / d ,u / dg = C u if u is even, 2 0 even L (R) ?\G. | ||
| 650 | |a Formes automorphes | ||
| 650 | |a Opérateurs pseudo-différentiels | ||
| 650 | |a Théorie des opérateurs | ||
| 650 | |a Nombres, Théorie des | ||
| 650 | |a Physique mathématique | ||
| 776 | 0 | |t Quantization and Arithmetic |b Texte imprimé |z 9783764398378 | |
| 776 | 0 | |0 137115997 |t Quantization and arithmetic |f André Unterberger |c Basel |n Birkhäuser |d 2008 |p 1 vol. (147 p.) |s Pseudo-Differential Operators |z 978-3-7643-8790-7 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-3-7643-8791-4 |z Accès sur la plateforme de l'éditeur | |
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