On the existence of a compactly supported Lp-solution for two-dimensional two-scale dilation equations
Kotowicz, Jarosław
Applicationes Mathematicae, Tome 24 (1997), p. 325-334 / Harvested from The Polish Digital Mathematics Library
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Necessary and sufficient conditions for the existence of compactly supported Lp-solutions for the two-dimensional two-scale dilation equations are given.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:219174 
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     author = {Jaros\l aw Kotowicz},
     title = {On the existence of a compactly supported $L^{p}$-solution for two-dimensional two-scale dilation equations},
     journal = {Applicationes Mathematicae},
     volume = {24},
     year = {1997},
     pages = {325-334},
     zbl = {0946.39009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv24i3p325bwm}
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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, Tome 24 (1997) pp. 325-334. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv24i3p325bwm/

[000] [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. | Zbl 0767.65002

[001] [2] D. Colella and C. Heil, The characterization of continuous, four-coefficient scaling functions and wavelets, IEEE Trans. Inform. Theory 30 (1992), 876-881. | Zbl 0743.42012

[002] [3] D. Colella and C. Heil, Characterization of scaling functions, I. Continuous solutions, J. Math. Anal. Appl. 15 (1994), 496-518. | Zbl 0797.39006

[003] [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. | Zbl 0882.42025

[004] [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. | Zbl 0763.42018

[005] [6] I. Daubechies and J. Lagarias, Two-scale difference equation II. Local regularity, infinite products of matrices, and fractals, ibid. 23 (1992), 1031-1079. | Zbl 0788.42013

[006] [7] T. Eirola, Sobolev characterization of solution of dilation equations, ibid. 23 (1992), 1015-1030. | Zbl 0761.42014

[007] [8] K. S. Lau and M. F. Ma, The regularity of Lp-scaling functions, preprint. | Zbl 0894.42013

[008] [9] K. S. Lau and J. Wang, Characterization of Lp-solutions for the two-scale dilation equations, SIAM J. Math. Anal. 26 (1995), 1018-1048. | Zbl 0828.42024