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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 1, 1998, pp. 159–181
DOI: 10.4171/ZAA/814

Published online: 1998-03-31

On the Solution of an Integral-Functional Equation with a Parameter

Lothar Berg[1] and Manfred Krüppel[2]

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

For a homogeneous integral-functional equation containing a parameter, we show existence and uniqueness of a compactly supported solution with given value for its integral. The solution is infinitely often differentiable, symmetric with respect to the point 1/2, monotonous at both sides of 1/2 and satisfies further functional equations. The Fourier series of the periodic continuation is determined. We also investigate spectral properties of the integral equation and find surprising connections between the Laplace transform of the eigenfunction and the eigenfunctions of the adjoint equation, and also directly between different eigenfunc-tions both in the compact and in the non-compact case. Moreover, asymptotic considerations are made.

Keywords: Integral-functional equations, Fourier series, spectral properties, biorthogonal sequences, Appell polynomials, asymptotic approximations

Berg Lothar, Krüppel Manfred: On the Solution of an Integral-Functional Equation with a Parameter. Z. Anal. Anwend. 17 (1998), 159-181. doi: 10.4171/ZAA/814