{"product_id":"9781461264682","title":"Progress in Mathematics: Hardy’s Theorem on Lie Groups","description":"\u003ch1\u003eProgress in Mathematics: Hardy’s Theorem on Lie Groups\u003c\/h1\u003e \u003ch2\u003eThangavelu, Sundaram\u003c\/h2\u003e \u003cp\u003eIn 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer­ sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that \"a f and g [= j] cannot both be very small\". ... The theo­ pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- \/2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- \/ ), then f = j = Ae- \/ , where A is a constant; and if one x 2 2 is0(e- \/ ), then both are null.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-10-12\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461264682\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-0-8176-8164-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 174\u003c\/p\u003e ","brand":"Birkhäuser Boston","offers":[{"title":"Default Title","offer_id":44316759425164,"sku":"9781461264682","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461264682.jpg?v=1775736380","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781461264682","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}