Multidimensional integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients

Deundyak, V. M.

doi:10.1134/s000143461005007x

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…The following theorem is a generalization of some results obtained for operators with homogeneous kernels (see [1], [3]). Theorem 1.…”

Section: Boundedness Theorem For Operators With Ah Kernels In Weighmentioning

confidence: 69%

“…In their papers assumptions of invariance under diagonal action of group SO(n) were imposed and considerably used in addition to homogeneity conditions. New broad class of operators with kernels of compact type including the set of SO(n)-invariant kernels was introduced and investigated in [3]. In [4] the results of [3] on boundedness and Fredholm property are expanded to the case of operators with anisotropically homogeneous kernels.…”

Section: Introductionmentioning

confidence: 99%

“…New broad class of operators with kernels of compact type including the set of SO(n)-invariant kernels was introduced and investigated in [3]. In [4] the results of [3] on boundedness and Fredholm property are expanded to the case of operators with anisotropically homogeneous kernels. The purpose of the present paper is to extend results related to boundedness and invertibility to the case of weighted L p -spaces.…”

Section: Introductionmentioning

confidence: 99%

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Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Miroshnikova¹

2014

AIP Conference Proceedings

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In weighted space L p (R n , ρ), 1 < p < ∞, a new broad class of integral operators with anisotropically homogeneous kernels is investigated. For such operators boundedness theorem is proved. Also the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type is considered. For elements of the algebra symbolic calculation is constructed, the invertibility criterion is obtained in terms of operator symbol.

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“…The following theorem is a generalization of some results obtained for operators with homogeneous kernels (see [1], [3]). Theorem 1.…”

Section: Boundedness Theorem For Operators With Ah Kernels In Weighmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Miroshnikova¹

2014

AIP Conference Proceedings

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“…Кроме условий однородности в данных работах на ядра накладывались и существенно использовались условия инвариантности относительно диагонального действия группы ортогональных преобразований SO(n). В [3,4] рассматривались классы ядер компактного и сингулярного типа, включающие в себя SO(n)-инвариантные ядра, а также методами теории операторов локального [5] и билокального типа [6] исследовалась разрешимость операторов с однородными ядрами и переменными коэффициентами. Топологические свойства пространств обратимых и фредгольмовых операторов из этого класса изучались в [7].…”

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FREDHOLM PROPERTY OF COMPOSITE TWO-DIMENSIONAL INTEGRAL OPERATORS WITH HOMOGENEOUS SINGULAR-TYPE KERNELS IN pL SPACE

Deundyak

Romanenko

2014

Vestnik Donskogo gosudarstvennogo tehničeskogo universiteta

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The authors have previously studied two - dimensional Fredholm integral operators with homogeneous kernels of fiber - singular type. For this class of operators, the symbolic calculus is built using the theory of biloc al operators by V. Pilidi, and Fredholm criterion is formulated through the inversibility of t wo families: the family of one - dimensional convolution operators, and the family of one - dimensional singular integral operators with continuous coefficients. The aim of this work is to study composite two - dimensional integral operators with homogeneous ker nels of fiber singular type analogous to Simonenko’s continual convolution integral operators. This investigation is a part of a more general study of algebra of operators with homogeneous kernels which layers are singular operat ors with piecewise continuo us coefficients. For the considered operators, the symbolic calculus and the necessary and sufficient Fredholm conditions are obtained.

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On Multidimensional Integral Operators with Homogeneous Kernels in Classes with Asymptotics

Avsyankin

2021

Operator Theory and Harmonic Analysis

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Multidimensional integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients

Cited by 6 publications

References 5 publications

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

FREDHOLM PROPERTY OF COMPOSITE TWO-DIMENSIONAL INTEGRAL OPERATORS WITH HOMOGENEOUS SINGULAR-TYPE KERNELS IN pL SPACE

On Multidimensional Integral Operators with Homogeneous Kernels in Classes with Asymptotics

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