Injectivity classes of the Pompeiu transformation

DOI10.1007/S11253-013-0758-XzbMath1281.44006OpenAlexW2169083844WikidataQ122946990 ScholiaQ122946990MaRDI QIDQ362513

Oksana Aleksandrovna Ochakovskaya

Publication date: 22 August 2013

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-013-0758-x

zbMATH Keywords

injectivity classesintegral ball meansPompeiu transformation

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Cites Work

• On the injectivity of the Pompeiu transform for integral ball means
• Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group
• Majorants of functions with zero integrals over balls of fixed radius
• Fourier analysis and determining sets for Radon measures on \({\mathbb{R}}^ n\)
• Pompeiu's problem on symmetric spaces
• Differentiation of integrals in \(\mathbb{R}^n\)
• Spherical means and CR functions on the Heisenberg group
• On functions with zero integrals over balls of fixed radius on a half-space.
• Precise characterizations of admissible rate of decrease of a non-trivial function with zero ball means
• Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
• Solution of the support problem for several function classes
• Injectivity sets of the Pompeiu transform
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