THE HANKEL––KIPRIANOV––KATRAKHOV TRANSFORM AND SINGULAR K–PSEUDODIFFERENTIAL OPERATORS
https://doi.org/10.25587/2411-9326-2024-1-21-34
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 '3m (Sobolev–Kipriyanov function spaces) and a theorem on products and commutators are proved.
About the Author
Yu. N. Bulatov
Bunin Yelets State University,
Russian Federation
Russian Federation
28.1 Kommunarov Street, 399770 Yelets, Lipetsk Region
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Review
For citations:
Bulatov Yu.N. THE HANKEL––KIPRIANOV––KATRAKHOV TRANSFORM AND SINGULAR K–PSEUDODIFFERENTIAL OPERATORS. Mathematical notes of NEFU. 2024;31(1):21-34. (In Russ.) https://doi.org/10.25587/2411-9326-2024-1-21-34
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