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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The interval of resolvent-positivity
for the biharmonic operator


Author: Michael Ulm
Journal: Proc. Amer. Math. Soc. 127 (1999), 481-489
MSC (1991): Primary 34L40, 35B50, 47A10
MathSciNet review: 1468205
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Abstract: For an operator $A$ on a Banach lattice we examine the interval on the real line for which the resolvent $\left( \lambda - A \right)^{-1}$ is positive. This positivity interval is then explicitly calculated for the biharmonic operator $A f = - f''''$ with three different boundary conditions.


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Additional Information

Michael Ulm
Affiliation: Abteilung Mathematik V, Universität Ulm, D-89069 Ulm, Germany
Email: ulm@mathematik.uni-ulm.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04556-6
PII: S 0002-9939(99)04556-6
Keywords: Biharmonic operator, resolvent-positivity
Received by editor(s): April 19, 1996
Received by editor(s) in revised form: May 22, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society