We describe all pairs of linear continuous operators that act in spaces of functions analytic in domains and satisfy a relation that is an operator analog of the Rubel equation.
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L. A. Rubel, “Derivation pairs on the holomorphic functions,” Funkc. Ekvac., No. 10, 225–227 (1967).
N. R. Nandakumar, “A note on derivation pairs,” Proc. Am. Math. Soc., No. 21, 535–539 (1969).
N. R. Nandakumar, “A note on the functional equation M(fg) = M(f)M(g) + L(f)L(g) on H(G),” Rend. Sem. Fac. Sci. Univ. Cagliari, 68, 13–17 (1998).
P. Kannappan and N. R. Nandakumar, “On a cosine functional equation for operators on the algebra of analytic functions in a domain,” Aequat. Math., 61, No. 3, 233–238 (2001).
D. H. Luecking and L. A. Rubel, Complex Analysis, a Functional Analysis Approach, Springer, New York (1984).
P. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York (2009).
G. K¨othe, “Dualit¨at in der Funktionentheorie,” J. Reine Angew. Math., 191, 30–49 (1953).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 12, pp. 1710–1716, December, 2011.
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Linchuk, Y.S. Operator generalization of one rubel’s result. Ukr Math J 63, 1945–1952 (2012). https://doi.org/10.1007/s11253-012-0623-3
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DOI: https://doi.org/10.1007/s11253-012-0623-3