Characterization of Eigenfunctions of the Laplacian by Boundedness Conditions

DOI10.2307/2154439zbMath0815.35012OpenAlexW4240007303MaRDI QIDQ3137509

Robert S. Strichartz

Publication date: 1 November 1993

Full work available at URL: https://doi.org/10.2307/2154439

zbMATH Keywords

harmonic analysisdoubly infinite sequence

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Analysis on other specific Lie groups (43A80)

Related Items (15)

A theorem of Roe and Strichartz on homogeneous trees ⋮ Paley-Wiener theorems for the two-sided quaternion Fourier transform ⋮ Mehler kernel approach to tempered distributions ⋮ Paley-Wiener theorems of generalized Fourier transform associated with a Cherednik type operator on the real line ⋮ Spectral theorems associated with the Cherednik operators on \(\mathbb R^d\) ⋮ Roe–Strichartz theorem on two‐step nilpotent Lie groups^a ⋮ Characterization of eigenfunctions of the Laplace-Beltrami operator using Fourier multipliers ⋮ Spectrum of functions and distributions for the Jacobi-Dunkl transform on \(\mathbb R\) ⋮ The fundamental theorem of simple harmonic functions ⋮ On the range of the generalized Fourier transform associated with a Cherednick type operator on the real line ⋮ Characterization of almost 𝐿^{𝑝}-eigenfunctions of the Laplace-Beltrami operator ⋮ SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS ⋮ L\({}^ p\) harmonic analysis and Radon transforms on the Heisenberg group ⋮ Characterization of the support for the hypergeometric Fourier transform of the \(W\)-invariant functions and distributions on \(\mathbb R ^d\) and Roe's theorem ⋮ On the range of the Opdam-Cherednik transform and Roe's theorem in the Cherednik setting

Cites Work

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• L\({}^ p\) harmonic analysis and Radon transforms on the Heisenberg group
• Harmonic analysis as spectral theory of Laplacians
• Fourier analysis on the Heisenberg group. I. Schwartz space
• A Note on Roe's Characterization of the Sine Function
• A characterization of the sine function
• Harmonic Analysis in Phase Space. (AM-122)
• Characterization of Eigenfunctions by Boundedness Conditions
• Tempered distributions with spectral gaps
• Tempered Distributions Supported on a Half-Space of R^N and Their Fourier Transforms

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