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The Structure of Functions

by Hans Triebel
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Current price ₹7,277.00
Original price ₹11,194.00
Original price ₹11,194.00
Original price ₹11,194.00
(-35%)
₹7,277.00
Current price ₹7,277.00

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Book cover type: Paperback
  • ISBN13: 9783034894944
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 425
  • Original Price: EUR 99.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 820 grams
  • BISAC Subject(s): Calculus, General, and Differential Equations / General

This 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.

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