Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori, Xiao Xiong, Quanhua Xu, Zhi Yin

Автор: Hans Triebel
Название: The Structure of Functions
ISBN: 3034805683 ISBN-13(EAN): 9783034805681
Издательство: Springer
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Описание: Dealing with the constructive Weierstrassian approach to the theory of function spaces and its various applications, this volume combines the advantages of atomic and wavelet representations to enhanced theories in spectral fractal elliptics and semi-linear equations.

Автор: Hans Triebel
Название: Theory of Function Spaces II
ISBN: 3764326395 ISBN-13(EAN): 9783764326395
Издательство: Springer
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Описание: Deals with the theory of function spaces of type Bspq and Fspq. This book analyzes the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds.

Автор: Hans Triebel
Название: The Structure of Functions
ISBN: 3034894945 ISBN-13(EAN): 9783034894944
Издательство: Springer
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Описание: 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.

Автор: H. Triebel
Название: Analysis and Mathematical Physics
ISBN: 9027720770 ISBN-13(EAN): 9789027720771
Издательство: Springer
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Автор: Ariel Barton, Svitlana Mayboroda
Название: Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces
ISBN: 1470419890 ISBN-13(EAN): 9781470419899
Издательство: Mare Nostrum (Eurospan)
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Описание: Presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable $t$-independent coefficients in spaces of fractional smoothness, in Besov and weighted $L^p$ classes. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

Автор: Vladimir Maz`ya
Название: Sobolev Spaces in Mathematics I
ISBN: 1441927573 ISBN-13(EAN): 9781441927576
Издательство: Springer
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Описание: This volume mark`s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

Название: Sobolev spaces in mathematics
ISBN: 0387856498 ISBN-13(EAN): 9780387856490
Издательство: Springer
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Описание: Sobolev spaces are the universal language of partial differential equations and mathematical analysis. This volume presents new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

Автор: Julii A. Dubinskii
Название: Sobolev Spaces of Infinite Order and Differential Equations
ISBN: 9027721475 ISBN-13(EAN): 9789027721471
Издательство: Springer
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