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Regularity of the multidimensional scaling functions: estimation of the $L^{p}$ -Sobolev exponent

Jarosław Kotowicz — 1999

Applicationes Mathematicae

The relationship between the spectral properties of the transfer operator corresponding to a wavelet refinement equation and the $L^{p}$ -Sobolev regularity of solution for the equation is established.

On the existence of a compactly supported $L^{p}$ -solution for two-dimensional two-scale dilation equations

Jarosław Kotowicz — 1997

Applicationes Mathematicae

Necessary and sufficient conditions for the existence of compactly supported $L^{p}$ -solutions for the two-dimensional two-scale dilation equations are given.

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Regularity of the multidimensional scaling functions: estimation of the L p -Sobolev exponent

On the existence of a compactly supported L p -solution for two-dimensional two-scale dilation equations

Regularity of the multidimensional scaling functions: estimation of the $L^{p}$ -Sobolev exponent

On the existence of a compactly supported $L^{p}$ -solution for two-dimensional two-scale dilation equations