Pseudo-differential operators associated with the Jacobi differential operator

DOI10.1006/jmaa.1997.5891zbMath0911.35129OpenAlexW2015867502MaRDI QIDQ1269654

K. Appert

Publication date: 26 October 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5891

zbMATH Keywords

Jacobi functionboundednessintegral representationFourier-Jacobi transform

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Pseudodifferential operators (47G30)

Related Items (26)

Pseudo-differential operator associated with quadratic-phase Fourier transform ⋮ The \(\mathrm{Y}\) transforms and allied pseudo-differential operators ⋮ Lebedev–Skalskaya transforms and allied operators on certain function spaces ⋮ The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces ⋮ Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ Two versions of pseudo-differential operators involving the Kontorovich-Lebedev transform in \(L^{2}(\mathbb{R}_{+};\frac{dx}{x})\) ⋮ The generalized Kontorovich-Lebedev transform and associated operators ⋮ Composition and commutator of pseudo-differential operators in the framework of zero-order Mehler-Fock transform domain ⋮ Integral representations of pseudo-differential operator associated with the Jacobi differential operator ⋮ A pair of Barut-Girardello type transforms and allied pseudo-differential operators ⋮ The convolution for zero-order Mehler–Fock transform and pseudo-differential operator ⋮ Sobolev-type spaces on the dual of the Chébli-Trimèche hypergroup and applications ⋮ Hardy-Littlewood-Sobolev-type inequality for the fractional Littlewood-Paley \(g\)-function in Jacobi analysis ⋮ Pseudo-differential operator in the framework of linear canonical transform domain ⋮ Psedidifferential-difference operators associated with dunkl operators ⋮ Hypoelliptic Jacobi convolution operators on Schwartz distributions ⋮ A pair of linear canonical Hankel transformations and associated pseudo-differential operators ⋮ Pseudo-differential operators involving Fractional Fourier cosine (sine) transform ⋮ Zero-order Mehler-Fock transform and Sobolev-type space ⋮ Lebedev–Skalskaya transforms on certain function spaces and associated pseudo-differential operators ⋮ Pseudo-differential operators associated with the Jacobi differential operator and Fourier-cosine wavelet transform ⋮ Composition of pseudo-differential operators associated with Kontorovich–Lebedev transform ⋮ Legendre functions, related Lebedev-Skalskaya transforms pairs and associated operators ⋮ A pair of pseudo-differential operators involving Hankel-type integral transformations ⋮ Boundedness of pseudo-differential operators involving Kontorovich–Lebedev transform ⋮ Sobolev type spaces associated with jacobi differential operators

Cites Work

• Transformation intégrale de Weyl et théorème de Paley-Wiener associes à un opérateur différentiel singulier sur \((0,\infty)\)
• Jacobi functions: the addition formula and the positivity of the dual convolution structure
• Convolution semigroups and central limit theorem associated with a dual convolution structure
• A class of pseudo-differential operators associated with Bessel operators
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• The convolution structure for Jacobi function expansions

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