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Wir sind gerne für Sie da(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
Produkteigenschaften
- Artikelnummer: 9783764387907
- Medium: Buch
- ISBN: 978-3-7643-8790-7
- Verlag: Springer
- Erscheinungstermin: 23.06.2008
- Sprache(n): Englisch
- Auflage: 2008
- Serie: Pseudo-Differential Operators
- Produktform: Kartoniert
- Gewicht: 284 g
- Seiten: 147
- Format (B x H x T): 170 x 240 x 9 mm
- Ausgabetyp: Kein, Unbekannt