Spectral properties of continuous refinement operators

Jia, R.; Lee, S.; Sharma, A.

doi:10.1090/S0002-9939-98-04006-4

Spectral properties of continuous refinement operators
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by R. Q. Jia, S. L. Lee and A. Sharma

Proc. Amer. Math. Soc. 126 (1998), 729-737

DOI: https://doi.org/10.1090/S0002-9939-98-04006-4

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Abstract:

This paper studies the spectrum of continuous refinement operators and relates their spectral properties with the solutions of the corresponding continuous refinement equations.

References

Charalambos D. Aliprantis and Owen Burkinshaw, Problems in real analysis, Academic Press, Inc., Boston, MA, 1990. A workbook with solutions. MR 1036729
Charles K. Chui and Xian Liang Shi, Continuous two-scale equations and dyadic wavelets, Adv. Comput. Math. 2 (1994), no. 2, 185–213. MR 1269380, DOI 10.1007/BF02521107
Wolfgang Dahmen and Charles A. Micchelli, Continuous refinement equations and subdivision, Adv. Comput. Math. 1 (1993), no. 1, 1–37. MR 1230249, DOI 10.1007/BF02070819
G. Derfel, N. Dyn, and D. Levin, Generalized refinement equations and subdivision processes, J. Approx. Theory 80 (1995), no. 2, 272–297. MR 1315413, DOI 10.1006/jath.1995.1019
N. Dyn and A. Ron, Multiresolution analysis by infinitely differentiable compactly supported functions, Appl. Comput. Harmon. Anal. 2 (1995), no. 1, 15–20. MR 1313096, DOI 10.1006/acha.1995.1002
T. N. T. Goodman, Charles A. Micchelli, and J. D. Ward, Spectral radius formulas for the dilation-convolution integral operator, Southeast Asian Bull. Math. 19 (1995), no. 1, 95–106. MR 1323419
Keiko Kabaya and Masao Iri, Sum of uniformly distributed random variables and a family of nonanalytic $C^\infty$-functions, Japan J. Appl. Math. 4 (1987), no. 1, 1–22. MR 899201, DOI 10.1007/BF03167752
K. Kabaya and M. Iri, On operators defining a family of nonanalytic $C^\infty$-functions, Japan J. Appl. Math. 5 (1988), 333–365.
V. A. Rvachëv, Compactly-supported solutions of functional-differential equations and their applications, Uspekhi Mat. Nauk 45 (1990), no. 1(271), 77–103, 222 (Russian); English transl., Russian Math. Surveys 45 (1990), no. 1, 87–120. MR 1050928, DOI 10.1070/RM1990v045n01ABEH002324
A. Sharma, Some simple properties of the up-function, Proc. Conf. at Aligarh (India) on Fourier Series, Approximation Theory and Applications (eds. Z. U. Ahmad, N. K. Govil, P. K. Jain), Wiley Eastern, New Delhi (to appear).