Nonstandard solvability for linear operators between sections of vector bundles
Author:
Hiroshi Akiyama
Journal:
Proc. Amer. Math. Soc. 128 (2000), 21292135
MSC (1991):
Primary 46S20, 03H05, 35D05, 47B38; Secondary 46F10, 47A50, 58G99.
Published electronically:
February 23, 2000
MathSciNet review:
1653401
Fulltext PDF Free Access
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Abstract: Given a certain kind of linear operator (possibly a differential operator or a properly supported pseudodifferential operator) between sections of Hermitian vector bundles over a Riemannian manifold, a necessary and sufficient condition is obtained for the operator to be solvable in a class of nonstandard sections in a generalized sense of weak solutions. The existence of a fundamentalsolutionlike internal section is established in the solvable case.
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Additional Information
Hiroshi Akiyama
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, Hamamatsu 4328561, Japan
Email:
tshakiy@eng.shizuoka.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993900052278
PII:
S 00029939(00)052278
Keywords:
Nonstandard analysis,
nonstandard extension,
transfer principle,
saturation principle,
hyperfinitedimensional internal vector space,
Hermitian vector bundle,
generalized section
Received by editor(s):
March 30, 1998
Received by editor(s) in revised form:
September 4, 1998
Published electronically:
February 23, 2000
Communicated by:
Carl G. Jockusch, Jr.
Article copyright:
© Copyright 2000
American Mathematical Society
