Matrix refinement equations: Continuity and smoothness
Czechoslovak Mathematical Journal (2007)
- Volume: 57, Issue: 2, page 747-762
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topHe, Xing-Gang, and Liu, Chun-Tai. "Matrix refinement equations: Continuity and smoothness." Czechoslovak Mathematical Journal 57.2 (2007): 747-762. <http://eudml.org/doc/31160>.
@article{He2007,
abstract = {In this paper we give some criteria for the existence of compactly supported $C^\{k+\alpha \}$-solutions ($k$ is an integer and $0\le \alpha <1$) of matrix refinement equations. Several examples are presented to illustrate the general theory.},
author = {He, Xing-Gang, Liu, Chun-Tai},
journal = {Czechoslovak Mathematical Journal},
keywords = {matrix refinement equation; continuity; smoothness; iteration; multi-wavelet; matrix refinement equation; continuity; smoothness; iteration; multi-wavelet},
language = {eng},
number = {2},
pages = {747-762},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Matrix refinement equations: Continuity and smoothness},
url = {http://eudml.org/doc/31160},
volume = {57},
year = {2007},
}
TY - JOUR
AU - He, Xing-Gang
AU - Liu, Chun-Tai
TI - Matrix refinement equations: Continuity and smoothness
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 747
EP - 762
AB - In this paper we give some criteria for the existence of compactly supported $C^{k+\alpha }$-solutions ($k$ is an integer and $0\le \alpha <1$) of matrix refinement equations. Several examples are presented to illustrate the general theory.
LA - eng
KW - matrix refinement equation; continuity; smoothness; iteration; multi-wavelet; matrix refinement equation; continuity; smoothness; iteration; multi-wavelet
UR - http://eudml.org/doc/31160
ER -
References
top- Stationary subdivision, Memoirs of Amer. Math. Soc., Vol. 93, 1991. (1991) MR1079033
- 10.1007/BF02649113, J. Fourier Anal. Appl. 3 (1997), 295–324. (1997) MR1448340DOI10.1007/BF02649113
- 10.1007/s003659900106, Constr. Approx. 15 (1999), 241–255. (1999) MR1668921DOI10.1007/s003659900106
- 10.1137/S0895479892225336, SIAM J. Matrix Anal. Appl. 15 (1994), 496–518. (1994) MR1266600DOI10.1137/S0895479892225336
- Matrix refinement equations: Existence and uniqueness, J. Fourier Anal. Appl. 2 (1996), 363–377. (1996) MR1395770
- 10.1137/0522089, Existence and global regularity of solutions SIAM J. Math. Anal. 22 (1991), 1388–1410. (1991) MR1112515DOI10.1137/0522089
- Two-scale difference equation II. Local regularity, infinite products of matrices, and fractals, SIAM J. Math. Anal. 22 (1991), 1388–1410. (1991) MR1112515
- 10.1137/S003614109630135X, SIAM J. Math. Anal. 29 4 (1998), 849–854. (1998) MR1617730DOI10.1137/S003614109630135X
- 10.1007/BF02510421, J. Fourier Anal. and Appli. 7 (2001), 143–167. (2001) MR1817673DOI10.1007/BF02510421
- 10.1137/S0036141092238771, SIAM J. Math. Anal. 26 (1995), 1018–1046. (1995) MR1338372DOI10.1137/S0036141092238771
- 10.1006/acha.1996.0018, Appl. Comp. Harmonic Anal. 3 (1996), 229–238. (1996) MR1400081DOI10.1006/acha.1996.0018
- Uniform refinement of curves Linear Algebra and Its Applications, 114/115 (1989), 841–870. (1989) MR0986909
- From wavelets to multiwavelets, Mathematical methods for curves and surfaces, 2 (Lillehammer) (1997), 375–399. (1997) MR1640571
- 10.1137/S0036141096302688, SIAM J. Math. Anal. 29 (1998), 235–250. (1998) Zbl0913.42028MR1617183DOI10.1137/S0036141096302688
- 10.1307/mmj/1029005707, Michigan Math. J. 44 (1997), 317–329. (1997) Zbl0901.42022MR1460417DOI10.1307/mmj/1029005707
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.