# A remark on multiresolution analysis of ${L}^{p}\left({\mathbb{R}}^{d}\right)$

Colloquium Mathematicae (1993)

- Volume: 66, Issue: 2, page 257-264
- ISSN: 0010-1354

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topSun, Qiyu. "A remark on multiresolution analysis of $L^{p}(ℝ^{d})$." Colloquium Mathematicae 66.2 (1993): 257-264. <http://eudml.org/doc/210247>.

@article{Sun1993,

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

author = {Sun, Qiyu},

journal = {Colloquium Mathematicae},

keywords = {local multipliers; stable integer translates; scaling function; wavelets; multiresolution analysis; globally linearly independent; refinement equation},

language = {eng},

number = {2},

pages = {257-264},

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

url = {http://eudml.org/doc/210247},

volume = {66},

year = {1993},

}

TY - JOUR

AU - Sun, Qiyu

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

JO - Colloquium Mathematicae

PY - 1993

VL - 66

IS - 2

SP - 257

EP - 264

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

LA - eng

KW - local multipliers; stable integer translates; scaling function; wavelets; multiresolution analysis; globally linearly independent; refinement equation

UR - http://eudml.org/doc/210247

ER -

## References

top- [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 ${L}^{2}\left({R}^{n}\right)$, in: Wavelets-A Tutorial in Theory and Applications, C. K. Chui (ed.), Academic Press, 1992, 259-294. Zbl0760.41030
- [3] S. Mallat, Multiresolution approximation and wavelet orthonormal bases of ${L}^{2}\left({R}^{n}\right)$, Trans. Amer. Math. Soc. 315 (1989), 69-88.
- [4] Y. Meyer, Ondelettes, fonctions spline et analyses graduées, Rapport CEREMADE 8703, 1987. Zbl0714.42022
- [5] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501
- [6] Q. Sun, Sequences spaces and stability of integer translates, Z. Anal. Anwendungen 12 (1993), 567-584. Zbl0801.46006

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