Analyticity and the Pompeiu problem

DOI10.1007/BF00250628zbMath0251.30047OpenAlexW2086751659MaRDI QIDQ2556960

Publication date: 1972

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00250628

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Other generalizations of analytic functions (including abstract-valued functions) (30G30) Monogenic and polygenic functions of one complex variable (30A05)

Related Items (75)

On a problem of Zalcman and its generalizations ⋮ Injectivity of the Pompeiu transform in the Heisenberg group ⋮ Spherical means and CR functions on the Heisenberg group ⋮ Analyticity on circles for rational and real-analytic functions of two real variables ⋮ A local version of the two-circles theorem ⋮ Liouville-type theorems for functions with zero integrals over balls of fixed radius ⋮ Analyticity on Curves ⋮ Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces ⋮ New mean value theorems for polyanalytic functions ⋮ Inversion of the local Pompeiu transform in real and complex hyperbolic spaces: Case of two balls ⋮ A local two radii theorem on the Chébli-Trimèche hypergroup ⋮ Symmetry theorems for the overdetermined eigenvalue problems ⋮ Le problème de la deconvolution ⋮ Inversion Theorems for the local Pompeiu transformation in the quaternion hyperbolic space ⋮ Morera-type theorems in the hyperbolic disc ⋮ Le problème de Pompeiu local. (Local Pompeiu problem) ⋮ Integrable harmonic functions on \(\mathbb{R}^ n\) ⋮ Analogues of the problem of analytic continuation from circles for some differential equations ⋮ Functions satisfying the mean value property in the limit ⋮ Pompeiu problem on product of Heisenberg groups ⋮ Integrals over circles passing through the origin and a characterization of analytic functions ⋮ Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs ⋮ On functions with zero integral moments over balls of fixed radius ⋮ Rellich type identities for eigenvalue problems and application to the Pompeiu problem ⋮ Morera theorems via microlocal analysis ⋮ A local two-radii theorem for quasianalytic classes of functions ⋮ Zalcman's problem and related two-radii theorems ⋮ ON ONE ZALCMAN PROBLEM FOR THE MEAN VALUE OPERATOR ⋮ On the one sided translates of powers of continuous functions on locally compact groups ⋮ Reconstruction of the Cauchy-Riemann operator by complex integration operators along circles ⋮ An inverse spectral theorem and its relation to the Pompeiu problem ⋮ Inverse load identification in vibrating nanoplates ⋮ A reconsideration of the 'three squares' problem ⋮ Isoparametric foliations and the Pompeiu property ⋮ Interpolation problems in \(C^ n\) with applications to harmonic analysis ⋮ Two-radii theorems for quasi-analytic classes of functions on a sphere ⋮ Convolution equations and mean-value theorems for solutions of linear elliptic equations with constant coefficients in the complex plane ⋮ Moment versions of the Morera problem in \(\mathbb C^n\) and \(\mathbb H^n\). ⋮ Criteria of holomorphy in symmetric domains ⋮ The pompeiu problem ⋮ On the translates of powers of a continuous periodic function ⋮ Unnamed Item ⋮ Parametric argument principle and its applications to CR functions and manifolds ⋮ Asymptotic expansions for a class of Fourier integrals and applications to the Pompeiu problem ⋮ Functions with zero integrals over cubes ⋮ How to find a measure from its potential ⋮ Analyticity on Rotation Invariant Families of Curves ⋮ Two-radius theorems for measure-preserving homemorphisms ⋮ Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group ⋮ Additional results of Zalcman's Pompeiu problem ⋮ A boundary Morera theorem ⋮ Harmonic analysis of spherical functions on \(SU(1,1)\) ⋮ Two radius support theorem for the sphere transform ⋮ Spherical means on two-point homogeneous spaces and applications ⋮ Characterization of polyanalytic functions by meromorphic extensions from chains of circles ⋮ Mean values and classes of harmonic functions ⋮ Pompeiu's problem on spaces of constant curvature ⋮ CR foliations, the strip-problem and Globevnik-Stout conjecture ⋮ The three-squares theorem for continuous functions ⋮ Analyticity of Almost Everywhere Differentiable Functions ⋮ The Pompeiu problem on locally symmetric spaces ⋮ A Morera type theorem for \(L^ 2\) functions in the Heisenberg group ⋮ On Schwartz's theorem for the motion group ⋮ Deformations of balls in Schiffer's conjecture for Riemannian symmetric spaces ⋮ Inversion of the local Pompeiu transform ⋮ Another step toward the solution of the pompeiu problem in the plane ⋮ Stability of the convex Pompeiu sets ⋮ Mean values and differential equations ⋮ Spectral synthesis and the Pompeiu problem ⋮ Morera theorems for complex manifolds ⋮ On invariant subspaces of continuous vector valued functions ⋮ Pompeiu transforms on geodesic spheres in real analytic manifolds ⋮ Boundary regularity for a family of overdetermined problems for the Helmholtz equation. ⋮ Saddle points and overdetermined problems for the Helmholtz equation ⋮ Morera type theorems on the unit disc

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