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On an exponential-cosine operator-valued functional equation. (English) Zbl 0334.39002


MSC:

39B52 Functional equations for functions with more general domains and/or ranges
47D03 Groups and semigroups of linear operators
47D99 Groups and semigroups of linear operators, their generalizations and applications
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References:

[1] Aczél, J.,Lectures on Functional Equations and Their Applications. Academic Press, New York-London 1966, [Math. in Science and Engineering, Vol. 19]. · Zbl 0139.09301
[2] Buche, A. B. andBharucha-Reid, A. T.,On Some Functional Equations Associated with Semigroups of Operators, Proc. Nat. Acad. Sci. U.S.A.60, 1170–1174 (1968). · Zbl 0159.44002 · doi:10.1073/pnas.60.4.1170
[3] Buche, A. B.,On the Cosine-sine Operator Functional Equations, Aequationes Math.6, 231–234 (1971). · Zbl 0232.47044 · doi:10.1007/BF01819756
[4] Hille, E. andPhillips, R. S.,Functional Analysis and Semi-groups. Amer. Math. Soc., Providence, R.I. 1957 [Amer. Math. Soc. Colloq. Publ. Vol. 31].
[5] Kurepa, S.,On Some Functional Equations in Banach Spaces, Studia Math.19, 149–158 (1960). · Zbl 0100.32702
[6] Kurepa, S.,A Cosine Functional Equation in Banach Algebras, Acta. Sci. Math. (Szeged)23, 255–267 (1962). · Zbl 0113.31702
[7] Sova, M.,Cosine Operator Functions. Panstwowe Wydawnictwo Naukowe, Warsaw 1966 [Rozprawy Mat., Vol.49]. · Zbl 0156.15404
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