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.

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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