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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A Fredholm theory for a class of first-order elliptic partial differential operators in $ {\bf R}\sp{n}$


Author: Homer F. Walker
Journal: Trans. Amer. Math. Soc. 165 (1972), 75-86
MSC: Primary 47F05; Secondary 35J99
MathSciNet review: 0291888
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Abstract: The objects of interest are linear first-order elliptic partial differential operators with domain $ {H_1}({R^n};{C^k})$ in $ {L_2}({R^n};{C^k})$, the first-order coefficients of which become constant and the zero-order coefficient of which vanishes outside a compact set in $ {R^n}$. It is shown that operators of this type are ``practically'' Fredholm in the following way: Such an operator has a finite index which is invariant under small perturbations, and its range can be characterized in terms of the range of an operator with constant coefficients and a finite index-related number of orthogonality conditions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0291888-3
PII: S 0002-9947(1972)0291888-3
Keywords: First-order elliptic operators, indices of elliptic operators, Fredholm operators
Article copyright: © Copyright 1972 American Mathematical Society