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The study of the fourier series of functions defined on moran fractals

The study of the fourier series of functions defined on moran fractals LetE be a Moran fractal andH s (E) denote thes-dimensional Hausdorff measure ofE. In this paper, we define a orthonormal and complete system φ of functions in the Hilbert spaceL 2(E,H s ) and prove that partial sums of the Fourier series, with respect to φ, of each functionf(x)∈L 1(E,H s ) converge tof(x) atH s -a.e.x∈E. Moreover, the Fourier series off, forf∈L p (E,H s ),p≥1, converges off inL p -norm. When Moran fractals degenerate into self-similar fractals, our results well agree with M. Reyes's results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The study of the fourier series of functions defined on moran fractals

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02015137
Publisher site
See Article on Publisher Site

Abstract

LetE be a Moran fractal andH s (E) denote thes-dimensional Hausdorff measure ofE. In this paper, we define a orthonormal and complete system φ of functions in the Hilbert spaceL 2(E,H s ) and prove that partial sums of the Fourier series, with respect to φ, of each functionf(x)∈L 1(E,H s ) converge tof(x) atH s -a.e.x∈E. Moreover, the Fourier series off, forf∈L p (E,H s ),p≥1, converges off inL p -norm. When Moran fractals degenerate into self-similar fractals, our results well agree with M. Reyes's results.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 15, 2005

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