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Systems of partial differential equations in the space of functions analytic in a ball and having given growth near its boundary. (English. Russian original) Zbl 0595.35101

Sib. Math. J. 26, 231-236 (1985); translation from Sib. Mat. Zh. 26, No. 2(150), 91-97 (1985).
Some spaces of analytic functions in a sphere and their duals are considered. This sphere is in \({\mathbb{C}}^ n\). Let \(\vec {\mathcal P}(\partial /\partial z)\) be a polynomial matrix operator. The author gives some necessary and sufficient conditions for the solvability of equation \(\vec {\mathcal P}(\partial /\partial z)\vec f=\vec g\), where \(\vec g\) is given.
Reviewer: W.Okrasiński

MSC:

35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
35A35 Theoretical approximation in context of PDEs
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
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References:

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