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2006 Characterization of wave front sets by wavelet transforms
Stevan Pilipović, Mirjana Vuletić
Tohoku Math. J. (2) 58(3): 369-391 (2006). DOI: 10.2748/tmj/1163775136

Abstract

We consider a special wavelet transform of Moritoh and give new definitions of wave front sets of tempered distributions via that wavelet transform. The major result is that these wave front sets are equal to the wave front sets in the sense of Hörmander in the cases $n=1, 2, 4, 8$. If $n\in \boldsymbol{N} \setminus \{1, 2, 4, 8\}$, then we combine results for dimensions $n=1, 2, 4, 8$ and characterize wave front sets in $\xi$-directions, where $\xi$ are presented as products of non-zero points of $\boldsymbol{R}^{n_1}, \dotsc, \boldsymbol{R}^{n_s}$, $n_1+ \dotsb +n_s=n, n_i \in \{1, 2, 4, 8\}$, $i=1, \dotsc, s$. In particular, the case $n=3$ is discussed through the fourth-dimensional wavelet transform.

Citation

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Stevan Pilipović. Mirjana Vuletić. "Characterization of wave front sets by wavelet transforms." Tohoku Math. J. (2) 58 (3) 369 - 391, 2006. https://doi.org/10.2748/tmj/1163775136

Information

Published: 2006
First available in Project Euclid: 17 November 2006

zbMATH: 1122.46021
MathSciNet: MR2273276
Digital Object Identifier: 10.2748/tmj/1163775136

Subjects:
Primary: 46F12
Secondary: ‎43A32

Rights: Copyright © 2006 Tohoku University

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Vol.58 • No. 3 • 2006
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