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By using the Heckman-Opdam theory on $\mathbb{R}^d$ given in [20], we define and study in this paper, the generalized wavelets on $\mathbb{R}^d$ and the generalized wavelet transform on $\mathbb{R}^d$, and we establish their properties. Next, we prove for the generalized wavelet transform Plancherel and inversion formulas.
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참고문헌 (20)
참고문헌 신청
L. C. Andrews / 1998 / Special functions of Mathematics for engineers / Oxford University Press
W.R.Bloom / 1995 / Harmonic analysis of probability measures on hyper-groups / Walter de Grayter
I.Cherednik / 1997 / Inverse Harish-Chandra transform and difference operators / Internat. Math. Res. Notices 15:733~750
L.Gallardo / 2012 / Positivity of the Jacobi-Cherednik intertwining operator and its dual / Adv. Pure Appl. Math 1:163~194
P.Goupilland / 1984 / Cycle octave and related transforms in seismic signal analysis / Geoexploration 23:85~102
W.R.Bloom / 1995 / Harmonic analysis of probability measures on hyper-groups / Walter de Grayter
I.Cherednik / 1997 / Inverse Harish-Chandra transform and difference operators / Internat. Math. Res. Notices 15:733~750
L.Gallardo / 2012 / Positivity of the Jacobi-Cherednik intertwining operator and its dual / Adv. Pure Appl. Math 1:163~194
P.Goupilland / 1984 / Cycle octave and related transforms in seismic signal analysis / Geoexploration 23:85~102
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