{"product_id":"9783764387907","title":"Pseudo-Differential Operators","description":"\u003ch1\u003ePseudo-Differential Operators\u003c\/h1\u003e \u003ch2\u003eUnterberger, André\u003c\/h2\u003e \u003cp\u003e(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\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2008-06-23\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783764387907\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-7643-8791-4\u003c\/p\u003e \u003cp\u003eDimensions: 240cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 147\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":46544956489868,"sku":"9783764387907","price":62.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783764387907.jpg?v=1775761859","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783764387907","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}