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On inversion of \(B\)-elliptic potentials by the method of Balakrishnan-Rubin. (English) Zbl 1044.35025

Summary: An inversion formula of Balakrashnan-Rubin type for the \(B\)-elliptic potentials is proved by using the formula representing Riesz potentials (\(B\)-elliptic potentials) associated with the Laplace-Bessel differential operator by means of the suitable Poisson semigroup.

MSC:

35J99 Elliptic equations and elliptic systems
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47B38 Linear operators on function spaces (general)
26A33 Fractional derivatives and integrals
44A35 Convolution as an integral transform
31B35 Connections of harmonic functions with differential equations in higher dimensions
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