A condition on a scaling function which generates a multiresolution analysis of is given.
@article{bwmeta1.element.bwnjournal-article-cmv66i2p257bwm, author = {Sun, Qiyu}, title = {A remark on multiresolution analysis of $L^{p}($\mathbb{R}$^{d})$ }, journal = {Colloquium Mathematicae}, volume = {66}, year = {1993}, pages = {257-264}, zbl = {0823.42018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv66i2p257bwm} }
Sun, Qiyu. A remark on multiresolution analysis of $L^{p}(ℝ^{d})$ . Colloquium Mathematicae, Tome 66 (1993) pp. 257-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv66i2p257bwm/
[000] [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.
[001] [2] W. R. Madych, Some elementary properties of multiresolution analysis of , in: Wavelets-A Tutorial in Theory and Applications, C. K. Chui (ed.), Academic Press, 1992, 259-294. | Zbl 0760.41030
[002] [3] S. Mallat, Multiresolution approximation and wavelet orthonormal bases of , Trans. Amer. Math. Soc. 315 (1989), 69-88.
[003] [4] Y. Meyer, Ondelettes, fonctions spline et analyses graduées, Rapport CEREMADE 8703, 1987. | Zbl 0714.42022
[004] [5] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. | Zbl 0207.13501
[005] [6] Q. Sun, Sequences spaces and stability of integer translates, Z. Anal. Anwendungen 12 (1993), 567-584. | Zbl 0801.46006