| Title:
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Recent developments in the theory of function spaces with dominating mixed smoothness (English) |
| Author:
|
Schmeisser, Hans-Jürgen |
| Language:
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English |
| Journal:
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Nonlinear Analysis, Function Spaces and Applications |
| Volume:
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Vol. 8 |
| Issue:
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2006 |
| Year:
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|
| Pages:
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145-204 |
| . |
| Category:
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math |
| . |
| Summary:
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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]. (English) |
| Keyword:
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Function spaces |
| Keyword:
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Fourier analysis |
| Keyword:
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dominating mixed smoothness |
| Keyword:
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hyperbolic cross approximation |
| Keyword:
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local means |
| Keyword:
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atoms |
| Keyword:
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wavelets |
| Keyword:
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embeddings |
| Keyword:
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traces |
| Keyword:
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entropy numbers |
| MSC:
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41A46 |
| MSC:
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42B25 |
| MSC:
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42B35 |
| MSC:
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42C40 |
| MSC:
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46E35 |
| MSC:
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47B06 |
| MSC:
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65T60 |
| . |
| Date available:
|
2009-10-08T09:52:13Z |
| Last updated:
|
2013-10-18 |
| Stable URL:
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http://hdl.handle.net/10338.dmlcz/702494 |
| . |
| Reference:
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