A remark on multiresolution analysis of $L^{p}(ℝ^{d})$

• Autorzy: Qiyu Sun
• Języki publikacji: EN

Abstrakty

EN

A condition on a scaling function which generates a multiresolution analysis of $L^p(ℝ^d)$ is given.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 66
• Numer: 2
• Strony: 257-264

Daty

wydano

1993

otrzymano

1992-10-20

poprawiono

1993-01-27

poprawiono

1993-03-29

Twórcy

autor

Qiyu Sun

• Center for Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, P.R. China

Bibliografia

• [1] R.-Q. Jia and C. A. Micchelli, Using the refinement equations for the construction of prewavelet II: power of two, in: Curves and Surfaces, P. J. Laurent, A. Le Mehaute and L. L. Schumaker (eds.), Academic Press, 1990, 1-36.
• [2] W. R. Madych, Some elementary properties of multiresolution analysis of $L^2(R^n)$, in: Wavelets-A Tutorial in Theory and Applications, C. K. Chui (ed.), Academic Press, 1992, 259-294.
• [3] S. Mallat, Multiresolution approximation and wavelet orthonormal bases of $L^2(R^n)$, Trans. Amer. Math. Soc. 315 (1989), 69-88.
• [4] Y. Meyer, Ondelettes, fonctions spline et analyses graduées, Rapport CEREMADE 8703, 1987.
• [5] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
• [6] Q. Sun, Sequences spaces and stability of integer translates, Z. Anal. Anwendungen 12 (1993), 567-584.