Abstract
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 \(|x|^{i\alpha }\). 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.
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This work is supported by the Ministry of Education and Science of Russia, Agreement No 075-02-2021-1386.
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To the memory of our teacher professor N. K. Karapetiants.
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Avsyankin, O.G., Ashikhmin, S.S. C*-ALGEBRA GENERATED BY INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS AND OSCILLATING COEFFICIENTS OF VARIOUS TYPES. J Math Sci 266, 66–76 (2022). https://doi.org/10.1007/s10958-022-05873-1
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DOI: https://doi.org/10.1007/s10958-022-05873-1
Keywords
- Integral operator
- Homogeneous kernel
- Oscillating coefficients
- \(C^*\)-algebra
- Group
- Symbol
- Fredholm property
- Invertibility