On the invariance of certain classes of functions under composition-Reference-Cited by-同舟云学术

On the invariance of certain classes of functions under composition

Published:1974 Issue:2 Volume:43 Page:345-348
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chaika Milton,Waterman Daniel

Abstract

Certain classes of functions are mapped into themselves by any change of variable. For some classes of this type which are of interest in the study of Fourier series, it is shown that the necessary and sufficient condition that g ∘ f g \circ f be in the class for each f f of that class is that g ∈ Lip ⁡ 1 g \in \operatorname {Lip} 1 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-043-02/S0002-9939-1974-0330367-9/S0002-9939-1974-0330367-9.pdf

Reference6 articles.

1. Functions whose Fourier series converge uniformly for every change of variable;Baernstein, Albert, II;Indiana Univ. Math. J.,1972

2. On some classes of continuous functions with convergent Fourier series;Garsia, A. M.;J. Math. Mech.,1964

3. Everywhere convergence of Fourier series;Goffman, Casper;Indiana Univ. Math. J.,1970

4. Functions whose Fourier series converge for every change of variable;Goffman, Casper;Proc. Amer. Math. Soc.,1968

5. C. O. Kiselman, On the Garsia-Sawyer condition for uniform convergence of Fourier series, Uppsala University, Dept. of Mathematics, Report No. 25, 1971.

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