A Fredholm theory for a class of first-order elliptic partial differential operators in $\textbf {R}^{n}$
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- by Homer F. Walker PDF
- Trans. Amer. Math. Soc. 165 (1972), 75-86 Request permission
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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 165 (1972), 75-86
- MSC: Primary 47F05; Secondary 35J99
- DOI: https://doi.org/10.1090/S0002-9947-1972-0291888-3
- MathSciNet review: 0291888