Pointwise and directional regularity of nonharmonic Fourier series
نویسندگان
چکیده
منابع مشابه
Pointwise and directional regularity of nonharmonic Fourier series
We investigate how the regularity of nonharmonic Fourier series is related to the spacing of their frequencies. This is obtained by using a transform which simultaneously captures the advantages of the Gabor and Wavelet transforms. Applications to the everywhere irregularity of solutions of some PDEs are given. We extend these results to the anisotropic setting in order to derive directional ir...
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The theory of nonharmonic Fourier series in L2(-ir,tr) is concerned with the completeness and expansion properties of sets of complex exponentials {e'x"'}. It is well known, for example, that the completeness of the set {e'x"'} ensures that of {e'^"'} whenever 2 lA„ ~~ M»l < oo. In this note we establish two results which guarantees that if {elX"'} is a Schauder basis for l}(—n, it), then [e'^"...
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In the early 19 century, J. Fourier was an impassioned advocate of the use of such sums, of course writing sines and cosines rather than complex exponentials. Euler, the Bernouillis, and others had used such sums in similar fashions and for similar ends, but Fourier made a claim extravagant for the time, namely that all functions could be expressed in such terms. Unfortunately, in those days th...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2010
ISSN: 1063-5203
DOI: 10.1016/j.acha.2010.02.002