On the null-spaces of first-order elliptic partial differential operators in $R\textbf {^{n}}$
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- by Homer F. Walker
- Proc. Amer. Math. Soc. 30 (1971), 278-286
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280864-7
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Abstract:
The objects to be studied are the null-spaces of 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 coefficients of which vanish outside a compact set in ${R^n}$. An example is given of an operator of this type which has a nontrivial null-space. It is shown that the dimension of the null-space of such an operator is finite for any number n of independent variables, and that this dimension is an upper-semicontinuous function of the operator in a certain sense.References
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- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- Peter D. Lax and Ralph S. Phillips, Scattering theory, Rocky Mountain J. Math. 1 (1971), no. 1, 173–223. MR 412636, DOI 10.1216/RMJ-1971-1-1-173
- Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 278-286
- MSC: Primary 35.44
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280864-7
- MathSciNet review: 0280864