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＜電子ブック＞
The Structure of Functions
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| 概要 | 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 ope...rators, 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.続きを見る |
| 目次 | I Decompositions of Functions 1 Introduction, heuristics, and preliminaries 2 Spaces on ?n: the regular case 3 Spaces on ?n: the general case 4 An application: the Fubini property 5 Spaces on domains: localization and Hardy inequalities 6 Spaces on domains. decompositions 7 Spaces on manifolds 8 Taylor expansions of distributions 9 Traces on sets, related function spaces and their decompositions II Sharp Inequalities 10 Introduction: Outline of methods and results 11 Classical inequalities 12 Envelopes 13 The critical case 14 The super-critical case 15 The sub-critical case 16 Hardy inequalities 17 Complements III Fractal Elliptic Operators 18 Introduction 19 Spectral theory for the fractal Laplacian 20 The fractal Dirichlet problem 21 Spectral theory on manifolds 22 Isotropic fractals and related function spaces 23 Isotropic fractal drums IV Truncations and Semi-linear Equations 24 Introduction 25 Truncations 26 The Q-operator 27 Semi-linear equations; the Q-method References Symbois.続きを見る |
| 本文を見る | Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive) |
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| 登録日 | 2020.06.27 |
| 更新日 | 2020.06.28 |