Lewy unsolvability and several complex variables.
Copyright policy )Lewy unsolvability and several complex variables.
The paper presents two new proofs of the unsolvability of certain partial differential equations of first order \(Lf=g\). Both proofs depend on the theory of holomorphic functions of several complex variables. In the first case the unsolvability of \(Lf=g\) results from the existence of peak points in the topological algebra that is the kernel of \(L\). The proof yields a removable singularities theorem for \(L\). The second proof depends on the extension property of Hartogs type. [See H. Lewy, Ann. Math. (2) 64, 514--522 (1956; Zbl 0074.06204).]
General theory of partial differential operators, 32D99, 35A07, Linear first-order PDEs, Geometric convexity in several complex variables, 32F40
General theory of partial differential operators, 32D99, 35A07, Linear first-order PDEs, Geometric convexity in several complex variables, 32F40
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