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Boundary value problems for linear systems†

Published online by Cambridge University Press:  14 November 2011

J. W. Neuberger
J. W. Neuberger
Affiliation:
North Texas State University, Denton, Texas, U.S.A.
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Synopsis

Suppose H and K are Hilbert spaces and H′0, H′ are closed subspaces of H so that H′0 ⊂ H′. Denote by P the orthogonal projection of H onto H′0, denote by g an element of k and by C a bounded linear transformation from H to K so that CC* = I, the identity on K. Denote CPC* by M. Given w in H′ one has the problem of finding u in H′ so that

There are given conditions on M (or certain operators related to M) which imply convergence of a certain iteratively generated sequence to a solution to this problem. The equation Cu = g represents an inhomogeneous system of linear differential equations (ordinary, partial or functional) and the condition P(u − w) = u − w is an abstract representation of inhomogeneous boundary conditions for u.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 297 - 302
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

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