Asymptotic expansions for a class of Fourier integrals and applications to the Pompeiu problem

DOI10.1007/BF02820458zbMath0737.35146OpenAlexW2049349791MaRDI QIDQ1177181

Nicola Garofalo, Fausto Segala

Publication date: 26 June 1992

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02820458

zbMATH Keywords

Fourier integralmethod of steepest descentasymptotic developmentdomain identificationPompeius problemreal analytic Jordan curves

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (5)

Fourier transform, null variety, and Laplacian's eigenvalues ⋮ Univalent Functions and the Pompeiu Problem ⋮ The covariogram and Fourier–Laplace transform in ℂⁿ ⋮ Another step toward the solution of the pompeiu problem in the plane ⋮ Stability of the convex Pompeiu sets

Cites Work

• An inverse spectral theorem and its relation to the Pompeiu problem
• A note on the Pompeiu problem for convex domains
• An overdetermined Neumann problem in the unit disk
• A partial solution of the Pompeiu problem
• The regularity of free boundaries in higher dimensions
• A symmetry problem in potential theory
• Remark on the preceding paper of Serrin
• Analyticity and the Pompeiu problem
• Spectral synthesis and the Pompeiu problem
• Symmetry Theorems Related to Pompeiu's Problem
• Seminar on Differential Geometry. (AM-102)
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