Laguerre expansions of tempered distributions and generalized functions

DOI10.1016/0022-247X(90)90205-TzbMath0715.46017MaRDI QIDQ752413

Antonio J. Duran

Publication date: 1990

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

zbMATH Keywords

Hankel transformconvolution algebraFourier-Laguerre coefficientsLaguerre expansions of tempered distributions and generalized functionsspace of rapidly decreasing sequencestempered distributions with positive support

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items (16)

\(C_0\)-semigroups and resolvent operators approximated by Laguerre expansions ⋮ Generalized functions and Laguerre expansions ⋮ Unnamed Item ⋮ \(G\)-type spaces of ultradistributions over \(\mathbb {R}^d_+\) and the Weyl pseudo-differential operators with radial symbols ⋮ Relations between Hermite and Laguerre expansions of ultradistributions over \(\mathbb R^d\) and \(\mathbb R^d_+\) ⋮ Fractional relaxation equations of distributed order ⋮ Numerical method for solving diffusion-wave phenomena ⋮ Asymptotics of Keiper-Li coefficients ⋮ Fractional powers of Hankel transforms in the Zemanian spaces ⋮ Functions with given moments and weight functions for orthogonal polynomials ⋮ Localization of Fréchet frames and expansion of generalized functions ⋮ On Hankel Transform ⋮ Spectral properties of Landau Hamiltonians with non-local potentials ⋮ Fractional differential equations through Laguerre expansions in abstract spaces: error estimates ⋮ A STRUCTURE THEOREM FOR THE SPACE $({G}^{\alpha}_{\alpha})^{\prime}$ ⋮ The Stieltjes Moments Problem for Rapidly Decreasing Functions

Cites Work

• Orthogonal series representations for generalized functions
• Orthonormal series expansions of certain distributions and distributional transform calculus
• On Zemanian's distributional eigenfunction transforms
• Eigenfunction expansion of generalized functions
• Summability of the Laguerre Polynomial Expansion of Generalized Functions
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