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

• Autorzy: Jarosław Kotowicz
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

dilation equation; compactly supported $L^p$ scaling function

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 3
• Strony: 325-334

Daty

wydano

1997

otrzymano

1996-05-28

poprawiono

1996-11-07

Twórcy

autor

Jarosław Kotowicz

• Institute of Mathematics, Warsaw University, Białystok Branch, Akademicka 2, 15-267 Białystok, Poland

Bibliografia

• [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.
• [2] D. Colella and C. Heil, The characterization of continuous, four-coefficient scaling functions and wavelets, IEEE Trans. Inform. Theory 30 (1992), 876-881.
• [3] D. Colella and C. Heil, Characterization of scaling functions, I. Continuous solutions, J. Math. Anal. Appl. 15 (1994), 496-518.
• [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.
• [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.
• [6] I. Daubechies and J. Lagarias, Two-scale difference equation II. Local regularity, infinite products of matrices, and fractals, ibid. 23 (1992), 1031-1079.
• [7] T. Eirola, Sobolev characterization of solution of dilation equations, ibid. 23 (1992), 1015-1030.
• [8] K. S. Lau and M. F. Ma, The regularity of $L^p$-scaling functions, preprint.
• [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.