Nonstandard solvability for linear operators between sections of vector bundles
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- by Hiroshi Akiyama PDF
- Proc. Amer. Math. Soc. 128 (2000), 2129-2135 Request permission
Abstract:
Given a certain kind of linear operator $A$ (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 $A$ to be solvable in a class of nonstandard sections in a generalized sense of weak solutions. The existence of a fundamental-solution-like internal section is established in the solvable case.References
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Additional Information
- Hiroshi Akiyama
- Affiliation: Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan
- Email: tshakiy@eng.shizuoka.ac.jp
- 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.
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2129-2135
- MSC (1991): Primary 46S20, 03H05, 35D05, 47B38; Secondary 46F10, 47A50, 58G99
- DOI: https://doi.org/10.1090/S0002-9939-00-05227-8
- MathSciNet review: 1653401