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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2021.1
- 수록면
- 371 - 381 (11page)
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In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for station ary and non-stationary wavelets) to construct the scaling function for L2(G) and, using the scaling function, we construct an orthonormal wavelet basis for L2(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.
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참고문헌 (29)
참고문헌 신청
D. Barbieri / 2017 / Tiling by lattices for locally compact abelian groups / C. R. Math 355:193~199
J. J. Benedetto / 2004 / A wavelet theory for local fields and related groups / J. Geom. Anal 14(3):423~456
J. J. Benedetto / 1999 / The construction multiple dyadic minimally supportrd frequency wavelets on R d , The functional and harmonic analysis of wavelets and frames / Amer. Math. Soc :43~74
M. Bownik / 2003 / Riesz wavelets and generalized multiresolution analysis / Appl. Comput. Harmonic. Anal 14(3):181~194
M. Bownik / 2017 / On Wilson bases in L 2(R d) / SIAM J. Math. Anal 49(5):3999~4023
J. J. Benedetto / 2004 / A wavelet theory for local fields and related groups / J. Geom. Anal 14(3):423~456
J. J. Benedetto / 1999 / The construction multiple dyadic minimally supportrd frequency wavelets on R d , The functional and harmonic analysis of wavelets and frames / Amer. Math. Soc :43~74
M. Bownik / 2003 / Riesz wavelets and generalized multiresolution analysis / Appl. Comput. Harmonic. Anal 14(3):181~194
M. Bownik / 2017 / On Wilson bases in L 2(R d) / SIAM J. Math. Anal 49(5):3999~4023
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