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We study the limit behavior of the spectral characteristics of truncated multidimensional integral operators whose kernels are homogeneous of degree –n and invariant under the rotation group SO(n). We prove that the limit of the -pseudospectra of the truncated operators K
as 0 is equal to the union of the -pseudospectra of the original operator K and the transposed operator
. 相似文献
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A. N. Karapetyants V. S. Rabinovich N. L. Vasilevski 《Integral Equations and Operator Theory》2001,40(3):278-308
We describe the Fredholm symbol algebra for theC
*-algebra generated by two dimensional singular integral operators, acting onL
2(2), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin.These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.Rostov State University RussiaPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-EPartially supported by CONACYT Project 27934-E, México. 相似文献
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Grand and small Bergman spaces of functions holomorphic in the unit disc are introduced. The boundedness of the Bergman projection operator on grand Bergman spaces is proved. The main result consists of estimates for functions in grand and small Bergman spaces near the boundary, which differ from those in the case of the classical Bergman space by a logarithmic multiplier with positive (for grand spaces) or negative (for small spaces) exponent. 相似文献
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Functional Analysis and Its Applications - This paper studies spaces of distributions on a dyadic half-line, which is the positive half-line equipped with bitwise binary addition and Lebesgue... 相似文献
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Zhirayr Avetisyan Alexey Karapetyants 《Mathematical Methods in the Applied Sciences》2023,46(1):811-829
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The concept of homogeneity is associated with transformations of a measure—measure dilations, which are most natural in the context of our general research scheme. For the study of integral operators, the notions of weak and strong homogeneity of the kernel are introduced. The weak case is proved to generate a homogeneous operator in the sense of our definition, while the stronger condition corresponds to the most relevant specific examples—classes of homogeneous integral operators on various metric spaces—and allows us to obtain an explicit general form for the kernels of such operators. The examples given in the article—various specific cases—illustrate general statements and results given in the paper and at the same time are of interest in their own way. 相似文献
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Mathematical Notes - We give a proof of the boundedness of the Bergman projection in generalized variable-exponent vanishing Morrey spaces over the unit disc and the upper half-plane. To this end,... 相似文献
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We consider twisted convolution operators with kernels having singularities on a sphere and having as Fourier transform the oscillatory symbol mα(|ξ|) = |ξ|–αei|ξ|, 0 ≤ ??α < 2n. We give integral representations for such operators and, as a principal result, we study Lp–Lq estimates for them. 相似文献