-compact operators.
A characterisation of dilation-analytic operators
A continuity in the weak topologies of a vector integral operator.
A dispersion inequality in the Hankel setting
The aim of this paper is to prove a quantitative version of Shapiro's uncertainty principle for orthonormal sequences in the setting of Gabor-Hankel theory.
A heat approximation
The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.
A note on an integral operator involving Legendre functions
A note on weak estimates for oscillating kernels
A probabilistic approach to the boundedness of singular integral operators
A proof of the smoothing properties of the positive part of Boltzmann's kernel.
We give two direct proofs of Sobolev estimates for the positive part of Boltzmann's kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.
A result about imbedded eigenvalues in the operator valued Friedrichs model
A weighted estimate for an intermediate operator on the cone of nonnegative functions.
About one two-dimensional special linear integral equation of the third kind.
About the Lp-Boundedness of Integral Operators with Kernels of the Form K1 (x-y)K2(x+y).
An application of Markov operators in differential and integral equations
An inversion problem for singular integral operators on homogeneous groups
Approximation by nonlinear integral operators in some modular function spaces
Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function is estimated, where and K satisfies a generalized Lipschitz condition with respect to the second variable.
Asymptotic behavior of singular values of certain integral operators.
Automorphisms of C commuting with partial integration operators in a rectangle
Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.
Beschränkte Integraloperatoren auf streng q-konvexen Gebieten in Cn.
BIE model of periodic diffraction problems in optics
Optical diffraction on a periodical interface belongs to relatively lowly exploited applications of the boundary integral equations method. This contribution presents a less frequent approach to the diffraction problem based on vector tangential fields of electromagnetic intensities. The problem is formulated as the system of boundary integral equations for tangential fields, for which existence and uniqueness of weak solution is proved. The properties of introduced boundary operators with singular...