Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group

DOI10.1007/s11854-008-0031-7zbMath1152.43006OpenAlexW2079678964MaRDI QIDQ948858

Vitalii Vladimirovich Volchkov, Valery Vladimirovich Volchkov

Publication date: 16 October 2008

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

Full work available at URL: https://doi.org/10.1007/s11854-008-0031-7

zbMATH Keywords

homogeneous spacesConvolution equationtwo-radii theoremPompeiu propertysymmetric spaces of arbitrary rank

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Analysis on other specific Lie groups (43A80)

Related Items (3)

Injectivity classes of the Pompeiu transformation ⋮ Zalcman's problem and related two-radii theorems ⋮ Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish

Cites Work

• Inversion of the local Pompeiu transform
• A local version of the two-circles theorem
• Le problème de Pompeiu local. (Local Pompeiu problem)
• Convolution equations in multidimensional spaces
• Pompeiu's problem on symmetric spaces
• Spherical means and CR functions on the Heisenberg group
• The Pompeiu problem on locally symmetric spaces
• Mean periodic functions on phase space and the Pompeiu problem with a twist
• Inversion of the local Pompeiu transform in real and complex hyperbolic spaces: Case of two balls
• Analyticity and the Pompeiu problem
• Mean values and differential equations
• Spectral synthesis and the Pompeiu problem
• Théorie générale des fonctions moyenne-périodiques
• Inversion de la transformation de pompéiu locale dans l'espace hyperbolique quaternionique – cas des deux boules
• Offbeat Integral Geometry
• Theorems on ball mean values in symmetric spaces
• Uniqueness theorems for solutions of the convolution equation on symmetric spaces
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