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The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces

Castro L. P., Natroshvili D.

Opuscula Mathematica

2006

Vol. 26, no. 2

289-303

We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain reactance conditions are assumed on it. Operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type operators are constructed and associated to the problem. At the end, the well-posedness of the problem is shown for a range of regularity orders of the Bessel potential spaces, and for a set of possible reactance numbers (dependent on the wave number).

Sequences of bounded φ-variation and weighted unconditional convergence of series

Musielak J.

Demonstratio Mathematica

2005

Vol. 38, nr 1

153--162

There are investigated spaces v0,φ of sequences of bounded φ-variation. Spaces v0, φ are applied to the problem of weighted unconditional convergence of series. It is shown that (vo,φ,lφ* ), where lφ* means the Orlicz sequence space generated by the N-function φ*, is a pair of weighted unconditional convergence. There are also considered nonlinear convolution - type operators in v0,φ .