Abstract:
To study problems with the singular differential Bessel operator B−γ with a negative parameter −γ ∈ (−1, 0), the paper introduces an integral transformation based on the solution u=Jµ of the singular Bessel equation B−γ u+u=0, which is expressed through the Bessel function of the first kind with a positive parameter µ= γ+1 . An
even and an odd K-Bessel (Hankel–Kipriyanov–Katrakhov) transform as well as a class of singular K-pseudodifferential operators are constructed. The main theorems on the orders of singular K-pseudodifferential operators with symbol from Ξm (Sobolev–Kipriyanov function spaces) and a theorem on products and commutators are proved.
Keywords:singular pseudodifferential operator, Hankel–Kipriyanov–Katrakhov transform, generalized pseudoshift, order of operators
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