Aliev, Ilham A.; Bayrakci, Simten On inversion of \(B\)-elliptic potentials by the method of Balakrishnan-Rubin. (English) Zbl 1044.35025 Fract. Calc. Appl. Anal. 1, No. 4, 365-384 (1998). 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. Cited in 13 Documents 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 Keywords:generalized shift; \(B\)-elliptic potentials; Riesz potentials; Laplace-Bessel differential operator; Poisson semigroup PDFBibTeX XMLCite \textit{I. A. Aliev} and \textit{S. Bayrakci}, Fract. Calc. Appl. Anal. 1, No. 4, 365--384 (1998; Zbl 1044.35025)