C-ALGEBRA GENERATED BY INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS AND OSCILLATING COEFFICIENTS OF VARIOUS TYPES

C-ALGEBRA GENERATED BY INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS AND OSCILLATING COEFFICIENTS OF VARIOUS TYPES

We consider the C*-algebra, generated by multidimensional integral operators with homogeneous degree ( - n ) kernels and by the operators of multiplication by radial weak oscillating functions and by oscillating functions of the form | x | i α . For this algebra, an operator symbolic calculus is con...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022, Vol.266 (1), p.66-76
Hauptverfasser: Avsyankin, Oleg G., Ashikhmin, Sergey S.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Kernels
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiplication
Operators (mathematics)
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Zusammenfassung:We consider the C*-algebra, generated by multidimensional integral operators with homogeneous degree ( - n ) kernels and by the operators of multiplication by radial weak oscillating functions and by oscillating functions of the form | x | i α . For this algebra, an operator symbolic calculus is constructed. In terms of this calculus, necessary and sufficient conditions for the Fredholm property of an operator are obtained.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05873-1