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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 2, 2001, pp. 457–488
DOI: 10.4171/ZAA/1025

Published online: 2001-06-30

Eigenfunctions of Two-Scale Difference Equations and Appell Polynomials

Lothar Berg[1] and Manfred Krüppel[2]

(1) Universität Rostock, Germany
(2) Universität Rostock, Germany

Both classical and distributional solutions of two-scale difference equations are interpreted as eigenfunctions, which are closely connected with Appell polynomials. Different generating functions are analyzed and the relations between them. Equivalent eigenfunctions as well as equivalent and minimal characteristic polynomials are defined and investigated in detail via the rational solution of a basic functional equation. Finally, reversed eigenfunctions are introduced and characterized.

Keywords: Two-scale difference equations, distributional solutions, eigenvalue problems, Appell polynomials, basic functional equation, equivalent and reversed eigenfunctions, minimal characteristic polynomials, sums of shifted eigenfunctions

Berg Lothar, Krüppel Manfred: Eigenfunctions of Two-Scale Difference Equations and Appell Polynomials. Z. Anal. Anwend. 20 (2001), 457-488. doi: 10.4171/ZAA/1025