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This article is cited in 6 scientific papers (total in 6 papers)
On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients
O. G. Avsyankin, V. M. Deundyak Rostov State University
Abstract:
In this paper, we study the Banach algebra $\mathfrak B$ generated by multidimensional integral operators whose kernels are homogeneous functions of degree $(-n)$ invariant with respect to the rotation group $SO(n)$ and by the operators of multiplication by radial weakly oscillating functions. A symbolic calculus is developed for the algebra $\mathfrak B$. The Fredholm property and the formula for calculating the index are described in terms of this calculus.
Keywords:
Fredholm property, integral operators, operator algebra, index of a Fredholm operator, Banach algebra, locally oscillating function.
Received: 27.02.2006 Revised: 22.09.2006
Citation:
O. G. Avsyankin, V. M. Deundyak, “On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients”, Mat. Zametki, 82:2 (2007), 163–176; Math. Notes, 82:2 (2007), 141–152
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https://www.mathnet.ru/eng/mzm3799https://doi.org/10.4213/mzm3799 https://www.mathnet.ru/eng/mzm/v82/i2/p163
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Abstract page: | 567 | Full-text PDF : | 230 | References: | 57 | First page: | 8 |
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