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A heat approximation

Miroslav Dont (2000)

Applications of Mathematics

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 proof of the smoothing properties of the positive part of Boltzmann's kernel.

François Bouchut, Laurent Desvillettes (1998)

Revista Matemática Iberoamericana

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.

Approximation by nonlinear integral operators in some modular function spaces

Carlo Bardaro, Julian Musielak, Gianluca Vinti (1996)

Annales Polonici Mathematici

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 f ( L ( G ) ) ϱ + η D o m T is estimated, where ( T f ) ( s ) = G K ( t - s , f ( t ) ) d t and K satisfies a generalized Lipschitz condition with respect to the second variable.

Automorphisms of C commuting with partial integration operators in a rectangle

Svetlana Mincheva (2000)

Banach Center Publications

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.

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