Juan Arias de Reyna's Books

Pointwise Convergence of Fourier Series

By: Juan Arias de Reyna

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Pointwise Convergence of Fourier Series

By: Juan Arias de Reyna

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

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Page Count

180

Publisher

Springer

Published Date

ISBN 10

3540458220

ISBN 13

9783540458227

C^\infinity - Differentiable Spaces

By: Juan A. Navarro González,Juan B. Sancho de Salas

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C^\infinity - Differentiable Spaces

By: Juan A. Navarro González,Juan B. Sancho de Salas

The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.

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Page Count

212

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354020072X

ISBN 13

9783540200727

Hamiltonian Reduction by Stages

By: Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor S. Ratiu

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Hamiltonian Reduction by Stages

By: Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor S. Ratiu

This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.

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527

Publisher

Springer

Published Date

ISBN 10

3540724702

ISBN 13

9783540724704

Pointwise Convergence of Fourier Series

By: Juan Arias de Reyna

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Pointwise Convergence of Fourier Series

By: Juan Arias de Reyna

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

180

Publisher

Springer

Published Date

ISBN 10

3540458220

ISBN 13

9783540458227

Book's by Juan Arias de Reyna

Pointwise Convergence of Fourier Series

Pointwise Convergence of Fourier Series

C^\infinity - Differentiable Spaces

C^\infinity - Differentiable Spaces

Hamiltonian Reduction by Stages

Hamiltonian Reduction by Stages

Pointwise Convergence of Fourier Series

Pointwise Convergence of Fourier Series

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