Functions with derivative in a Hardy space

Elijah Liflyand

doi:10.1007/978-3-030-04429-9_2

Functions with derivative in a Hardy space

Elijah Liflyand

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

As explained above, we are going to study separately the cosine Fourier transform $$ \hat{f}_c (x) = \int^\infty_\mathrm{0} f(t)\, \mathrm{cos}\, xt \, dt$$ and the sine Fourier transform $$ \hat{f}_s (x) = \int^\infty_\mathrm{0} f(t)\, \mathrm{sin}\, xt \, dt,$$ and their integrability properties.

Original language	English
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	57-83
Number of pages	27
DOIs	https://doi.org/10.1007/978-3-030-04429-9_2
State	Published - 2019

Publication series

Name	Applied and Numerical Harmonic Analysis
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

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10.1007/978-3-030-04429-9_2

Cite this

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title = "Functions with derivative in a Hardy space",

abstract = "As explained above, we are going to study separately the cosine Fourier transform \$\$ \textbackslash{}hat\{f\}\_c (x) = \textbackslash{}int\textasciicircum{}\textbackslash{}infty\_\textbackslash{}mathrm\{0\} f(t)\textbackslash{}, \textbackslash{}mathrm\{cos\}\textbackslash{}, xt \textbackslash{}, dt\$\$ and the sine Fourier transform \$\$ \textbackslash{}hat\{f\}\_s (x) = \textbackslash{}int\textasciicircum{}\textbackslash{}infty\_\textbackslash{}mathrm\{0\} f(t)\textbackslash{}, \textbackslash{}mathrm\{sin\}\textbackslash{}, xt \textbackslash{}, dt,\$\$ and their integrability properties.",

author = "Elijah Liflyand",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

doi = "10.1007/978-3-030-04429-9\_2",

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N2 - As explained above, we are going to study separately the cosine Fourier transform $$ \hat{f}_c (x) = \int^\infty_\mathrm{0} f(t)\, \mathrm{cos}\, xt \, dt$$ and the sine Fourier transform $$ \hat{f}_s (x) = \int^\infty_\mathrm{0} f(t)\, \mathrm{sin}\, xt \, dt,$$ and their integrability properties.

AB - As explained above, we are going to study separately the cosine Fourier transform $$ \hat{f}_c (x) = \int^\infty_\mathrm{0} f(t)\, \mathrm{cos}\, xt \, dt$$ and the sine Fourier transform $$ \hat{f}_s (x) = \int^\infty_\mathrm{0} f(t)\, \mathrm{sin}\, xt \, dt,$$ and their integrability properties.

UR - https://www.scopus.com/pages/publications/85063340504

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BT - Applied and Numerical Harmonic Analysis

PB - Springer International Publishing

ER -

Functions with derivative in a Hardy space

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