Abstract
The paper introduces integral transformations for studying problems with a singular differential Bessel operator \(B_{-\gamma_{i}}\) with a negative parameter \(-1<-\gamma_{i}<0\). We construct the \(\mathbf{J}\)-Bessel transform and the corresponding class of singular \(\mathbf{J}\)-pseudodifferential operators. A theorem on the order of \(\mathbf{J}\)-pseudodifferential operators in a special class of Sobolev–Kipriyanov functions is proved.
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Notes
One of the authors of this work knows for sure that these studies were carried out for at least two years. V. Katrakhov, already in the zero years of this century, answered the question about the lack of relevant publications that there was a problem with a certain construction that should play the role of ‘‘shift’’, but it is arranged so ‘‘incorrectly’’ that it does not allow applying it to differential equations.
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Lyakhov, L.N., Bulatov, Y.N. Composition and Commutator of Singular \(\boldsymbol{\mathbf{J}}\)-Pseudodifferential Kipriyanov Operators in \(\boldsymbol{\mathbb{R}_{N}}\). Lobachevskii J Math 44, 3438–3454 (2023). https://doi.org/10.1134/S199508022308036X
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DOI: https://doi.org/10.1134/S199508022308036X