De Rham's singular function, two-scale difference equations and Appell polynomials

DOI10.1007/BF03322429zbMath0954.39017OpenAlexW2073399025MaRDI QIDQ1578454

Manfred Krüppel, Lothar Berg

Publication date: 31 August 2000

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03322429

zbMATH Keywords

waveletfunctional equationsAppell polynomialsdifference equationfunctional-integral equationalmost everywhere zero derivativesde Rham's singular function

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Other nonlinear integral equations (45G10) Lipschitz (Hölder) classes (26A16) Singular functions, Cantor functions, functions with other special properties (26A30) Functional equations for real functions (39B22) Additive difference equations (39A10) Appell, Horn and Lauricella functions (33C65)

Related Items

On conjugacies between asymmetric Bernoulli shifts ⋮ Unnamed Item ⋮ Eigenfunctions of two-scale difference equations and Appell polynomials ⋮ A new approach with new solutions to the Matkowski and Wesołowski problem

Cites Work

• Unnamed Item
• Unnamed Item
• Uniform refinement of curves
• Cantor sets and integral-functional equations
• Compactly supported solutions of two-scale difference equations
• Functional equations and nowhere differentiable functions
• Functional equations for peculiar functions
• On the solution of an integral-functional equation with a parameter
• De Rham's singular function and related functions
• Compactly supported solutions of functional-differential equations and their applications
• Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions
• The characterization of continuous, four-coefficient scaling functions and wavelets
• Ten Lectures on Wavelets
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• On the Regularity of Matrix Refinable Functions
• Characterizations of Scaling Functions: Continuous Solutions