Pointwise Fourier inversion on tori and other compact manifolds

DOI10.1007/BF01261638zbMath0938.42007OpenAlexW1966337876MaRDI QIDQ1808999

Michael E. Taylor

Publication date: 15 June 2000

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

Full work available at URL: https://eudml.org/doc/59618

zbMATH Keywords

Fourier seriesGibbs phenomenoneigenfunction expansion

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Wave equation (35L05) Summability in several variables (42B08) Fourier integral operators applied to PDEs (35S30)

Related Items (15)

On pointwise convergence of Fourier series of the Indicator function of \(D\) dimensional ball ⋮ THE GIBBS PHENOMENON, THE PINSKY PHENOMENON, AND VARIANTS FOR EIGENFUNCTION EXPANSIONS ⋮ On spectral expansions of piecewise smooth functions depending on the geodesic distance ⋮ On the Pinsky phenomenon for B-elliptic operators ⋮ Riemann localisation on the sphere ⋮ On the Pinsky phenomenon ⋮ Pointwise Fourier inversion—An addendum ⋮ Dependence of the convergence domain of spectral expansions on the geometry of the set of discontinuity of the function being expanded ⋮ On multiple Fourier series of piecewise smooth functions ⋮ Eigenfunction expansions and the Pinsky phenomenon on compact manifolds ⋮ On summability of eigenfunction expansions of piecewise smooth functions ⋮ On the summability of spectral expansions of piecewise smooth functions ⋮ Unnamed Item ⋮ On eigenfunction expansions of piecewise smooth functions, associated with the power of the Schrödinger operator ⋮ Fourier expansions of functions with bounded variation of several variables

Cites Work

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• Number of lattice points in families of homothetic domains in \(R^ n\)
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Fourier series of radial functions in several variables
• The Gibbs phenomenon for multiple Fourier integrals
• Pointwise Fourier inversion: A wave equation approach
• Localization and convergence of eigenfunction expansions
• The spectral function of an elliptic operator
• Pointwise fourier inversion and related eigenfunction expansions

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