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1

Duals of homogeneous weighted sequence Besov spaces and applications

Huang P.-K., Wang K.

Journal of Applied Analysis

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2011

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Vol. 17, nr 2

181-205

EN

In this article, we study the duals of homogeneous weighted sequence Besov spaces b α,q p,w, where the weight w is non-negative and locally integrable. In particular, when 0 < p < 1, we find a type of new sequence spaces which characterize the duals of b α,q p,w. Also, we find the necessary and sufficient conditions for the boundedness of diagonal matrices acting on homogeneous weighted sequence Besov spaces. Using these results, we give some applications to characterize the boundedness of Fourier-Haar multipliers and paraproduct operators. In this situation, we need to require that the weight w is an Ap weight.

2

Application of the M RBV S classes to embedding relations of the Besov classes

Szal B.

Demonstratio Mathematica

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2009

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Vol. 42, nr 2

303-322

EN

L. Leindler obtained a necessary and sufficient condition in order to a function is an element of Lp having Fourier coefficients of rest bounded variation belong to the Besov class. In the present paper the analogue of this result is proved with function having Fourier coefficients of mean rest bounded variation. We also discuss embedding relations between the Besov classes.

3

Błędy pomiarów transmitancji z pseudolosowymi sygnałami wymuszającymi

Giżewski S., Krzywaźnia A., Ociepka J.

Przegląd Włókienniczy - Włókno, Odzież, Skóra

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2008

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nr 7

27-30

EN

Methods of measurement of spectral transfer function based on wide-band testing signals have been investigated since 70'th of the last century. The methods are attractive practically as they offer possibility of determination of transfer function in many frequency points basing on only one realization of measurement procedure. Now a few typical solutions are practically used that are based on using binary or ternary pseudorandom sequences, synthesized multi-sine and impulse signals. The impulse and binary or ternary pseudorandom sequences signals have spectral power density function corresponding to a squared-sinc function (sinx/x)2, which leads to aliasing errors if sampling technique and digital signal processing are employed. The primary task of the paper is estimation of measuring errors of transfer function of linear inertial objects when pseudorandom binary or ternary sequences of maximum length are used as the test signals. Particularly, influence of parameters of sampling analog-to-digital conversion and object parameters (order, corner frequency) on measuring uncertainty has been investigated by means of computer simulation. Selection of sampling frequency selection has been considered.

4

Properties of Fourier coefficients of spline wavelets

Šimsová J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

101-106

EN

Periodic B-spline functions have got many useful properties. Especially it is the property of its Fourier coefficients. In this article it is introduced and proved a similar property of Fourier coefficients of spline wavelets.