The continuous wavelet transform associated with a differential-difference operator and applications

zbMath1189.42018MaRDI QIDQ969225

Hatem Mejjaoli, Nadia Sraieb

Publication date: 12 May 2010

Published in: Communications in Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.cma/1271890717

zbMATH Keywords

differential-difference operatorgeneralized continuous wavelet transformpractical real inversion formulasreproducing kernel inversion formulas

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Other transforms and operators of Fourier type (43A32) Reflection groups, reflection geometries (51F15)

Related Items (1)

Generalized convolution operator associated with the \((k, a)\)-generalized Fourier transform on the real line and applications

Cites Work

• Inversion of the Lions transmutation operators using generalized wavelets
• Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\)
• Heisenberg inequalities for Jacobi transforms
• Heisenberg uncertainty principle on Chébli-Trimèche hypergroups
• Hardy and Cowling-price theorems associated with a Dunkl type differential-difference operator on the real line
• Uncertainty principles for the continuous Dunkl Gabor transform and the Dunkl continuous wavelet transform
• Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
• Integral Kernels with Reflection Group Invariance
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$
• One approach to some general integral transforms and its applications

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