{"product_id":"the-structure-of-functions-9783034894944","title":"The Structure of Functions","description":"\u003cp\u003e • Author(s): Hans Triebel\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Calculus\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier- strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m): m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N . One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . m E C. This resembles, at least formally, the Weier- strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45284482187415,"sku":"9783034894944","price":7277.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783034894944.webp?v=1769281309","url":"https:\/\/atlanticbooks.com\/products\/the-structure-of-functions-9783034894944","provider":"Atlantic Books","version":"1.0","type":"link"}