On a Kipriyanov problem for a singular ultrahyperbolic equation

We obtain a differential equation for the spherical means generated by a multidimensional generalized shift of an arbitrary smooth “even” function. We study the Asgeirsson property of solutions of a singular ultrahyperbolic equation that includes singular differential operators Δ B acting in Euclide...

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Bibliographic Details
Published in:Differential equations 2014-04, Vol.50 (4), p.513-525
Main Authors: Lyakhov, L. N., Polovinkin, I. P., Shishkina, E. L.
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Differential equations
Inverse
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Studies
Theorems
Variables
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Summary:We obtain a differential equation for the spherical means generated by a multidimensional generalized shift of an arbitrary smooth “even” function. We study the Asgeirsson property of solutions of a singular ultrahyperbolic equation that includes singular differential operators Δ B acting in Euclidean spaces, in general, of distinct dimensions. We represent the structure of a “radial” solution of the considered equation. A theorem similar to the Asgeirsson inverse theorem is proved.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266114040090