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1998-1999 | 25 | 4 | 431-447
Tytuł artykułu

Regularity of the multidimensional scaling functions: estimation of the $L^{p}$-Sobolev exponent

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The relationship between the spectral properties of the transfer operator corresponding to a wavelet refinement equation and the $L^p$-Sobolev regularity of solution for the equation is established.
Rocznik
Tom
25
Numer
4
Strony
431-447
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-11-18
poprawiono
1998-03-06
Twórcy
  • Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
Bibliografia
  • [1] N. K. Bari, Trigonometric Series, Fizmatgiz, 1961 (in Russian).
  • [2] A. Cohen and I. Daubechies, A new technique to estimate the regularity of refinable functions, Rev. Mat. Iberoamericana 12 (1996), 527-591.
  • [3] A. Cohen and R. D. Ryan, Wavelets and Multiscale Signal Processing, Appl. Math. Math. Comput. 11, Chapman & Hall, 1995.
  • [4] I. Daubechies and J. Lagarias, Two-scale difference equation I. Existence and global regularity of solutions, SIAM J. Math. Anal. 22 (1991), 1388-1410.
  • [5] I. Daubechies and J. Lagarias, Two-scale difference equation II. Local regularity, infinite products of matrices, and fractals, ibid. 23 (1992), 1031-1079.
  • [6] K. Deimling, Nonlinear Functional Analysis, Springer, 1985.
  • [7] T. Eriola, Sobolev characterization of solution of dilation equations, SIAM J. Math. Anal. 23 (1992), 1015-1030.
  • [8] C. Heil and D. Colella, Sobolev regularity for refinement equations via ergodic theory, in: C. K. Chui and L. L. Schumaker (eds.), Approximation Theory VIII, Vol. 2, World Sci., 1995, 151-158.
  • [9] P. N. Heller and R. O. Wells Jr., The spectral theory of multiresolution operators and applications, in: Wavelets: Theory, Algorithms, and Applications, C. K. Chui, L. Montefusco and L. Puccio (eds.), Wavelets 5, Academic Press, 1994, 13-31.
  • [10] L. Hervé, Construction et régularité des fonctions d'échelle, SIAM J. Math. Anal. 26 (1995), 1361-1385.
  • [11] J. Kotowicz, On existence of a compactly supported $L^p$ solution for two-dimensional two-scale dilation equations, Appl. Math. (Warsaw) 24 (1997), 325-334.
  • [12] 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.
  • [13] C. A. Micchelli and H. Prautzsch, Uniform refinement of curves, Linear Algebra Appl. 114/115 (1989), 841-870.
  • [14] O. Rioul, Simple regularity criteria for subdivision schemes, SIAM J. Math. Anal. 23 (1992), 1544-1576.
  • [15] N. A. Sadovnichiĭ, Theory of Operators, Moscow Univ. Press, 1979 (in Russian).
  • [16] L. Villemoes, Energy moments in time and frequency for $2$-scale dilation equation solutions and wavelets, SIAM J. Math. Anal. 23 (1992), 1519-1543.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i4p431bwm
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