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A differential operator of infinite order with constant coefficients on a weighted space of entire functions. (English. Russian original) Zbl 0624.46028
Sov. Math., Dokl. 34, 24-26 (1987); translation from Dokl. Akad. Nauk SSSR 289, 33-35 (1986).
The commutative Banach algebra P generated by an operator of generalized differentiation on a Banach space B of entire functions with growth condition is discussed. Conditions for invertibility of members of P and an isomorphism of P with a convolution algebra are indicated.
Reviewer: J.P.Holmes
46G05 Derivatives of functions in infinite-dimensional spaces
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
47B38 Linear operators on function spaces (general)