Spectral properties of continuous refinement operators

DOI10.1090/S0002-9939-98-04006-4zbMath0897.41010OpenAlexW1574441008MaRDI QIDQ4383053

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Publication date: 24 March 1998

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-98-04006-4

zbMATH Keywords

eigenvaluesspectral radiusspectrumcompact operatorspower iterationup functioncontinuous refinement equationscontinuous refinement operatorsdilation constant

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) General harmonic expansions, frames (42C15) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Approximation by other special function classes (41A30) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (7)

Convergence speeds of iterations of Ruelle operator with weakly contractive IFS. ⋮ Refinement equations and distributional fixed points ⋮ Series expansions for the solutions of an integral-functional equation with a parameter ⋮ Refinement equations and Feller operators ⋮ Atomic functions: generalization to the multivariable case and promising applications ⋮ Probability distribution functions of the Grincevičjus series ⋮ The spectral radius of matrix continuous refinement operators

Cites Work

• Unnamed Item
• Multiresolution analysis by infinitely differentiable compactly supported functions
• Generalized refinement equations and subdivision processes
• Continuous refinement equations and subdivision
• Continuous two-scale equations and dyadic wavelets
• Spectral radius formulas for the dilation-convolution integral operator
• Sum of uniformly distributed random variables and a family of nonalyticC ∞-functions
• Compactly supported solutions of functional-differential equations and their applications
• On operators defining a family of nonanalyticC ∞-functions

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