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

Applicationes Mathematicae (1999)

- Volume: 25, Issue: 4, page 431-447
- ISSN: 1233-7234

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topKotowicz, Jarosław. "Regularity of the multidimensional scaling functions: estimation of the $L^{p}$-Sobolev exponent." Applicationes Mathematicae 25.4 (1999): 431-447. <http://eudml.org/doc/219217>.

@article{Kotowicz1999,

abstract = {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.},

author = {Kotowicz, Jarosław},

journal = {Applicationes Mathematicae},

keywords = {$L^p$-Sobolev exponent; transfer operator; refinement equation; scaling functions; spectral radius; -Sobolev exponent; wavelet refinement equation},

language = {eng},

number = {4},

pages = {431-447},

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

url = {http://eudml.org/doc/219217},

volume = {25},

year = {1999},

}

TY - JOUR

AU - Kotowicz, Jarosław

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

JO - Applicationes Mathematicae

PY - 1999

VL - 25

IS - 4

SP - 431

EP - 447

AB - 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.

LA - eng

KW - $L^p$-Sobolev exponent; transfer operator; refinement equation; scaling functions; spectral radius; -Sobolev exponent; wavelet refinement equation

UR - http://eudml.org/doc/219217

ER -

## References

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- [11] J. Kotowicz, On existence of a compactly supported ${L}^{p}$ solution for two-dimensional two-scale dilation equations, Appl. Math. (Warsaw) 24 (1997), 325-334. Zbl0946.39009
- [12] K. S. Lau and J. Wang, Characterization of ${L}^{p}$-solutions for the two-scale dilation equations, SIAM J. Math. Anal. 26 (1995), 1018-1048. Zbl0828.42024
- [13] C. A. Micchelli and H. Prautzsch, Uniform refinement of curves, Linear Algebra Appl. 114/115 (1989), 841-870. Zbl0668.65011
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