Recent developments in the theory of function spaces with dominating mixed smoothness

Schmeisser, Hans-Jürgen

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Institute of Mathematics of the Academy of Sciences of the Czech Republic(Praha), page 145-204

Abstract

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The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation with respect to hyperbolic crosses, embeddings and traces. We follow [42], [43], [44], [59], [63], [64], [70], and [94], [95], [96]. Partial results can be found also in [6], [7], [8], [37] and [48].

How to cite

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Schmeisser, Hans-Jürgen. "Recent developments in the theory of function spaces with dominating mixed smoothness." Nonlinear Analysis, Function Spaces and Applications. Praha: Institute of Mathematics of the Academy of Sciences of the Czech Republic, 2007. 145-204. <http://eudml.org/doc/221063>.

@inProceedings{Schmeisser2007,
abstract = {The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation with respect to hyperbolic crosses, embeddings and traces. We follow [42], [43], [44], [59], [63], [64], [70], and [94], [95], [96]. Partial results can be found also in [6], [7], [8], [37] and [48].},
author = {Schmeisser, Hans-Jürgen},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Function spaces; Fourier analysis; dominating mixed smoothness; hyperbolic cross approximation; local means; atoms; wavelets; embeddings; traces; entropy numbers},
location = {Praha},
pages = {145-204},
publisher = {Institute of Mathematics of the Academy of Sciences of the Czech Republic},
title = {Recent developments in the theory of function spaces with dominating mixed smoothness},
url = {http://eudml.org/doc/221063},
year = {2007},
}

TY - CLSWK
AU - Schmeisser, Hans-Jürgen
TI - Recent developments in the theory of function spaces with dominating mixed smoothness
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 2007
CY - Praha
PB - Institute of Mathematics of the Academy of Sciences of the Czech Republic
SP - 145
EP - 204
AB - The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation with respect to hyperbolic crosses, embeddings and traces. We follow [42], [43], [44], [59], [63], [64], [70], and [94], [95], [96]. Partial results can be found also in [6], [7], [8], [37] and [48].
KW - Function spaces; Fourier analysis; dominating mixed smoothness; hyperbolic cross approximation; local means; atoms; wavelets; embeddings; traces; entropy numbers
UR - http://eudml.org/doc/221063
ER -

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