Cargando…
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Birkhäuser Basel : Imprint: Birkhäuser,
2008.
|
| Edición: | 1st ed. 2008. |
| Colección: | Pseudo-Differential Operators, Theory and Applications,
1 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-7643-8791-4 | ||
| 003 | DE-He213 | ||
| 005 | 20220116193737.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2008 sz | s |||| 0|eng d | ||
| 020 | |a 9783764387914 |9 978-3-7643-8791-4 | ||
| 024 | 7 | |a 10.1007/978-3-7643-8791-4 |2 doi | |
| 050 | 4 | |a QA252.3 | |
| 050 | 4 | |a QA387 | |
| 072 | 7 | |a PBG |2 bicssc | |
| 072 | 7 | |a MAT014000 |2 bisacsh | |
| 072 | 7 | |a PBG |2 thema | |
| 082 | 0 | 4 | |a 512.55 |2 23 |
| 082 | 0 | 4 | |a 512.482 |2 23 |
| 100 | 1 | |a Unterberger, André. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Quantization and Arithmetic |h [electronic resource] / |c by André Unterberger. |
| 250 | |a 1st ed. 2008. | ||
| 264 | 1 | |a Basel : |b Birkhäuser Basel : |b Imprint: Birkhäuser, |c 2008. | |
| 300 | |a 147 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Pseudo-Differential Operators, Theory and Applications, |x 2297-0363 ; |v 1 | |
| 505 | 0 | |a Weyl Calculus and Arithmetic -- Quantization -- Quantization and Modular Forms -- Back to the Weyl Calculus. | |
| 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 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 1 | 4 | |a Topological Groups and Lie Groups. |
| 650 | 2 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 650 | 2 | 4 | |a Operator Theory. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783764398378 |
| 776 | 0 | 8 | |i Printed edition: |z 9783764387907 |
| 830 | 0 | |a Pseudo-Differential Operators, Theory and Applications, |x 2297-0363 ; |v 1 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-7643-8791-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||