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

Jarosław Kotowicz

Applicationes Mathematicae (1997)

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

Abstract

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

How to cite

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Kotowicz, 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

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  1. [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. [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. [3] D. Colella and C. Heil, Characterization of scaling functions, I. Continuous solutions, J. Math. Anal. Appl. 15 (1994), 496-518. Zbl0797.39006
  4. [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. [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. [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. [7] T. Eirola, Sobolev characterization of solution of dilation equations, ibid. 23 (1992), 1015-1030. Zbl0761.42014
  8. [8] K. S. Lau and M. F. Ma, The regularity of L p -scaling functions, preprint. Zbl0894.42013
  9. [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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