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On Schur complements and n-metaharmonic functions

Published online by Cambridge University Press:  14 November 2011

Edward C. Nichols  and
Ronald L. Smith
Edward C. Nichols
Affiliation:
Department of Mathematics, The University of Tennessee at Chattanooga Chattanooga, Tennessee 37403, U.S.A
Ronald L. Smith
Affiliation:
Department of Mathematics, The University of Tennessee at Chattanooga Chattanooga, Tennessee 37403, U.S.A
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Synopsis

Several properties of symmetric matrices and positive definite matrices are derived. These are used to improve an estimate given for regular solutions of the n-metaharmonic differential equation by Chow and Dunninger [1].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 3-4 , 1991 , pp. 233 - 240
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Chow, S. N. and Dunninger, D. R.. A maximum principle for n-metaharmoriic functions. Proc. Amer. Math. Soc. 43 (1974), no. 1, 79–83.Google Scholar
2Haynsworth, E. V.. Determination of the inertia of a partitioned Hermitian matrix. Linear Algebra Appl. 1 (1968), 73–81.CrossRefGoogle Scholar
3Lancaster, P.. Theory of Matrices (New York: Academic Press, 1969).Google Scholar
4Marcus, M. and Mine, H.. A Survey of Matrix Theory and Matrix Inequalities (Boston: Prindle, Weber, & Schmidt, 1964).Google Scholar
5Massera, J. L.. Contributions to stability theory. Ann. of Math. 64 (1956), 182–206.CrossRefGoogle Scholar
6Schur, J. [Issail]. Über Potenzreihen, die im Innern des Einheilskreises beschränkt sind. J. Reine Angew. Math. 147 (1917), 205–232.CrossRefGoogle Scholar
7Vekua, I. N.. New methods for solving elliptic equations (Moscow: OGIZ, 1948); English translation: Series in Appl. Math. 1 (Amsterdam: North-Holland and New York: Interscience, 1967).Google Scholar