| 書目名稱 | Quantization and Arithmetic | | 編輯 | André Unterberger | | 視頻video | http://file.papertrans.cn/782/781023/781023.mp4 | | 概述 | Consists entirely of new material.Contents is related to the book Automorphic pseudodifferential analysis and higher-level Weyl calculi (appeared in Progress in Mathematics) by the same author: one-di | | 叢書名稱 | Pseudo-Differential Operators | | 圖書封面 |  | | 描述 | (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 ,sinceonehasforsomeappropriatecon | | 出版日期 | Book 2008 | | 關(guān)鍵詞 | Matrix; Weyl calculus; calculus; coherent states; metaplectic representation; number theory; quantization | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-7643-8791-4 | | isbn_softcover | 978-3-7643-8790-7 | | isbn_ebook | 978-3-7643-8791-4Series ISSN 2297-0355 Series E-ISSN 2297-0363 | | issn_series | 2297-0355 | | copyright | Birkh?user Basel 2008 |
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