Tohoku Mathematical Journal

Characterization of wave front sets by wavelet transforms

Stevan Pilipović and Mirjana Vuletić

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2) Volume 58, Number 3 (2006), 369-391.

Dates
First available in Project Euclid: 17 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1163775136

Digital Object Identifier
doi:10.2748/tmj/1163775136

Mathematical Reviews number (MathSciNet)
MR2273276

Zentralblatt MATH identifier
1122.46021

Subjects
Primary: 46F12: Integral transforms in distribution spaces [See also 42-XX, 44-XX]
Secondary: 43A32: Other transforms and operators of Fourier type

Keywords
Wavelet transform wave front

Citation

Pilipović, Stevan; Vuletić, Mirjana. Characterization of wave front sets by wavelet transforms. Tohoku Math. J. (2) 58 (2006), no. 3, 369--391. doi:10.2748/tmj/1163775136. https://projecteuclid.org/euclid.tmj/1163775136.


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