Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Spectral properties of continuous
refinement operators


Authors: R. Q. Jia, S. L. Lee and A. Sharma
Journal: Proc. Amer. Math. Soc. 126 (1998), 729-737
MSC (1991): Primary 34K99, 41A15, 41A25, 41A30, 42C05, 42C15
DOI: https://doi.org/10.1090/S0002-9939-98-04006-4
MathSciNet review: 1416091
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. C. D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, Academic Press, San Diego, 1990. MR 91c:28002
  • 2. C. K. Chui and X. Shi, Continuous two-scale equations and dyadic wavelets, Advances in Comp. Math. 2 (1994), 185-213. MR 95d:42038
  • 3. W. Dahmen and C. A. Micchelli, Continuous refinement equations and subdivision, Advances in Comp. Math. 1 (1993), 1-37. MR 94h:41018
  • 4. G. Derfel, N. Dyn, and D. Levin, Generalized functional equations and subdivision processes, J. Approx. Theory 80 (1995), 272-297. MR 95k:45003
  • 5. N. Dyn and A. Ron, Multiresolution analysis by infinitely differentiable compactly supported functions, Applied and Computational Harmonic Analysis 2 (1995), 15-20. MR 95k:42057
  • 6. T. N. T. Goodman, C. A. Micchelli and J. D. Ward, Spectral radius formulas for the dilation-convolution integral operators, SEA Bull. Math. 19 (1995), 95-106. MR 96c:47042
  • 7. K. Kabaya and M. Iri, Sum of uniformly distributed random variables and a family of nonanalytic $C^\infty$-functions, Japan J. Appl. Math. 4 (1987), 1-22. MR 89d:26023
  • 8. K. Kabaya and M. Iri, On operators defining a family of nonanalytic $C^\infty$-functions, Japan J. Appl. Math. 5 (1988), 333-365.
  • 9. V. A. Rvachev, Compactly supported solutions of functional-differential equations and their applications, Russian Mathematical Survey, 45:1 (1990), 87-120. MR 91j:34104
  • 10. 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).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34K99, 41A15, 41A25, 41A30, 42C05, 42C15

Retrieve articles in all journals with MSC (1991): 34K99, 41A15, 41A25, 41A30, 42C05, 42C15


Additional Information

R. Q. Jia
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: jia@xihu.math.ualberta.ca

S. L. Lee
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
Email: matleesl@haar.math.nus.sg

A. Sharma
Email: asharma@vega.math.ualberta.ca

DOI: https://doi.org/10.1090/S0002-9939-98-04006-4
Keywords: Continuous refinement equations, up function, continuous refinement operators, compact operators, spectrum, spectral radius, eigenvalues, dilation constant, power iteration
Received by editor(s): October 25, 1995
Received by editor(s) in revised form: July 23, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society