Function Spaces and Wavelets on Domains

von

Triebel, Hans

BuchGebunden

265 Seiten

Englisch

European Mathematical Societyerschienen am15.08.2008

Wavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations.This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Especially, wavelet expansions and extensions to corresponding spaces on Euclidean n-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated.Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained.mehr

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KlappentextWavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations.This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Especially, wavelet expansions and extensions to corresponding spaces on Euclidean n-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated.Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained.

Details

ISBN/GTIN978-3-03719-019-7

ProduktartBuch

EinbandartGebunden

Verlag

European Mathematical Society

Erscheinungsjahr2008

Erscheinungsdatum15.08.2008

ReiheEMS Tracts in Mathematics

Reihen-Nr.7

Seiten265 Seiten

SpracheEnglisch