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

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 3, page 325-334
- ISSN: 1233-7234

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topKotowicz, Jarosław. "On the existence of a compactly supported $L^{p}$-solution for two-dimensional two-scale dilation equations." Applicationes Mathematicae 24.3 (1997): 325-334. <http://eudml.org/doc/219174>.

@article{Kotowicz1997,

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

author = {Kotowicz, Jarosław},

journal = {Applicationes Mathematicae},

keywords = {dilation equation; compactly supported $L^p$ scaling function; wavelet; compactly supported scaling function; two-scale dilation equations},

language = {eng},

number = {3},

pages = {325-334},

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

url = {http://eudml.org/doc/219174},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Kotowicz, Jarosław

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

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 3

SP - 325

EP - 334

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

LA - eng

KW - dilation equation; compactly supported $L^p$ scaling function; wavelet; compactly supported scaling function; two-scale dilation equations

UR - http://eudml.org/doc/219174

ER -

## References

top- [1] M. A. Berger and Y. Wang, Multidimensional two-scale dilation equations, in: Wavelets - A Tutorial in Theory and Applications, C. K. Chui (ed.), Wavelets 3, Academic Press, 1992, 295-323. Zbl0767.65002
- [2] D. Colella and C. Heil, The characterization of continuous, four-coefficient scaling functions and wavelets, IEEE Trans. Inform. Theory 30 (1992), 876-881. Zbl0743.42012
- [3] D. Colella and C. Heil, Characterization of scaling functions, I. Continuous solutions, J. Math. Anal. Appl. 15 (1994), 496-518. Zbl0797.39006
- [4] D. Colella and C. Heil, Dilation eqautions and the smoothness of compactly supported wavelets, in: Wavelets: Mathematics and Applications, J. J. Benedetto, M. W. Frazier (eds.), Stud. Adv. Math., CRC Press., 1994, 163-201. Zbl0882.42025
- [5] I. Daubechies and J. Lagarias, Two-scale difference equation I. Existence and global regularity of solutions, SIAM J. Math. Anal. 22 (1991), 1388-1410. Zbl0763.42018
- [6] I. Daubechies and J. Lagarias, Two-scale difference equation II. Local regularity, infinite products of matrices, and fractals, ibid. 23 (1992), 1031-1079. Zbl0788.42013
- [7] T. Eirola, Sobolev characterization of solution of dilation equations, ibid. 23 (1992), 1015-1030. Zbl0761.42014
- [8] K. S. Lau and M. F. Ma, The regularity of ${L}^{p}$-scaling functions, preprint. Zbl0894.42013
- [9] 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

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