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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

1Agmon, S.. Lectures on Elliptic Boundary Value Problems (Princeton, N.J.: van Nostrana, 1965).Google Scholar
2Halmos, P. R.. A Hilbert Space Problem Book (Princeton, N.J.: van Nostrana, 1967).Google Scholar
3Neuberger, J.. Projection Methods for Linear and Nonlinear Systems of Partial Differential Equations. Lecture Notes in Mathematics 564 (Berlin: Springor, 1976).Google Scholar
4Neuberger, J.. Square Integrable Solutions to Linear Inhomogeneous Systems. J. Differential Equations 27 (1978), 144–152.CrossRefGoogle Scholar
5Neuberger, J.. An Interative Method of Approximating Solutions to Nonlinear Partial Differential Equations. Proceedings of Conference on Applied Nonlinear Analysis, University of Texas at Arlington (to appear).Google Scholar
6Riesz, F. and Sz.-Nagy, B.. Functional Analysis (New York: Ungar, 1955).Google Scholar