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Expansion problems with irregular multipoint boundary conditions

Published online by Cambridge University Press:  14 November 2011

Gerhard Freiling
Gerhard Freiling
Affiliation:
Fachbereich Mathematik, Universität Duisburg
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Synopsis

Using asymptotic estimates for the Green's function of irregular multipoint eigenvalue problems, we state sufficient conditions for the uniform convergence of the expansion of functions into a series of eigenfunctions.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 235 - 246
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Eberhard, W.. Die Entwicklungen nach Eigenfunktionen irregulärer Eigenwertprobleme mit zerfallenden Randbedingungen. Math. Z. 86 (1964), 205–214.CrossRefGoogle Scholar
2Eberhard, W.. Die Entwicklungen nach Eigenfunktionen irregulärer Eigenwertprobleme mit zerfallenden Randbedingunen II. Math. Z. 90 (1965), 126–137.CrossRefGoogle Scholar
3Fage, M. K.. Operator-analytic functions of a single independant variable (russ.). Trudy Moskov. Mat. Obšč. 7 (1958), 227–268.Google Scholar
4Freiling, G.. Irregular multipoint eigenvalue problems. Math. Meth. Appl. Sci. 3 (1981), to appear.CrossRefGoogle Scholar
5Hromov, A. P.. Expansion in the characteristic functions of ordinary linear differential operators with nonregular decomposing boundary conditions. Mat. Sb. 70 (112), (1966), 310–329.Google Scholar
6Hromov, A. P.. On summability of expansions in the eigenfunctions for an ordinary differential equation with uncoupled boundary conditions and an analog of a theorem of Weierstrass. In Ordinary Differential Equations and Fourier Series Expansions (in Russian) (Saratovsk Univ., 1968).Google Scholar
7Hromov, A. P.. Differential operator with irregular splitting boundary conditions. Math. Notes 19 (1976), 451–456.CrossRefGoogle Scholar
8Kostyuchenko, A. G. and Shkalikov, A. A.. Summability of eigenfunction expansions of differential operators and convolution operators. Funkdonal. Anal, i Priložen. 12, No. 4, (1978), 24–40.Google Scholar
9Wolter, M.. Notwendige und hinreichende Kriterien für die Entwickelbarkeit von Funktionen in gleichmässig konvergente Fourierreihen nach den Eigenfunktionen einer Klasse N-irregulärer Eigenwertprobleme mit zerfallenden Randbedingungen (Dissertation, Marburg/Lahn, 1978).Google Scholar