Abstract
Let D be an analytic manifold of dimensionality 2,U(D) be the space of functions analytic on D with the topology of compact convergence, andϕ(z) be a function fromU(D). Under certain sufficiently general assumptions relative to the manifold D, in the note is found the general form of a continuous linear operator inU(D), commuting with the operator of multiplication by a functionϕ(z). Because of this it is established under what conditions each such operator is an operator of multiplication by some function.
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N. I. Nagnibida, “Operators which commute with operators of multiplication on analytic functions and quasi-exponential bases connected with them,” in: Theory of Functions, Functional Analysis and their Applications [in Russian], Vol. 13, 63–66 (1971).
G. Springer, Introduction to Riemann Surfaces, Addison-Wesley (1956).
H. Schaefer, Topological Vector Spaces, Springer-Verlag (1971).
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Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 269–276, February, 1973.
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Zakharyuta, V.P., Tsar'kov, M.Y. Operators commuting with multiplication in spaces of analytic functions of one variable. Mathematical Notes of the Academy of Sciences of the USSR 13, 164–167 (1973). https://doi.org/10.1007/BF01094236
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DOI: https://doi.org/10.1007/BF01094236