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Perturbational analysis of dual trigonometric series associated with boundary conditions of first and third kind

Published online by Cambridge University Press:  14 November 2011

Robert B. Kelman
Robert B. Kelman
Affiliation:
Department of Computer Science, Colorado State University, Fort Collins, and Department of Biometrics, University of Colorado Medical Center, Denver
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Synopsis

Existence and uniqueness theorems are established for dual trigonometric equations having right-hand sides that are given functions of bounded variation. The first equation in each pair has coefficients, say {Jn(n + h)} or (jn(n + h – ½)}, and the second equation coefficients {jn)}, where h is a nonnegative constant. A potential problem involving mixed boundary conditions of first and third kind is associated with each dual series. The potential problem is analysed using a stepwise perturbation procedure involving solutions in powers of h. The analysis demonstrates that the present dual series problem can be resolved if the dual series problem associated with the case h = 0 is solvable, the latter being a result obtained earlier.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 3-4 , 1978 , pp. 291 - 298
Copyright
Copyright © Royal Society of Edinburgh 1978

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