André Unterberger

Quantization and Arithmetic

• Broschiertes Buch

Produktbeschreibung

(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

---

Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Pseudo-differential Operators 1
• Verlag: Birkhäuser / Birkhäuser Basel / Springer, Basel
• Artikelnr. des Verlages: 12238552, 978-3-7643-8790-7
• 2008
• Seitenzahl: 160
• Erscheinungstermin: 23. Juni 2008
• Englisch
• Abmessung: 240mm x 170mm x 9mm
• Gewicht: 394g
• ISBN-13: 9783764387907
• ISBN-10: 3764387904
• Artikelnr.: 23519291

Inhaltsangabe

Weyl Calculus and Arithmetic.- Quantization.- Quantization and Modular Forms.- Back to the Weyl Calculus.