Abstract
We solve Van Vleck’s functional equation on semigroups with an involution in terms of multiplicative functions.
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Bahyrycz A., Brzdȩk J.: A note on d’Alembert’s functional equation on a restricted domain. Aequationes Math. 88(1–2), 169–173 (2014)
Berrone L.R., Dieulefait L.V.: A functional equation related to the product in a quadratic number field. Aequationes Math. 81(1–2), 167–175 (2011)
Bouikhalene B., Elqorachi E., Charifi A.: On the approximate solution of D’Alembert type equation originating from number theory. Extracta Math. 28(2), 157–167 (2013)
Chojnacki W.: On uniformly bounded spherical functions in Hilbert space. Aequationes Math. 81(1–2), 135–154 (2011)
Corovei I.: The functional equation f(xy) + f(yx) + f(xy −1) + f(y −1 x) = 4f(x)f(y) for nilpotent groups. (Romanian) Bul. Ştiinţ. Instit. Politehn. Cluj-Napoca Ser. Mat.-Fiz.-Mec. Apl. 20, 25–28 (1978)
Davison T.M.K.: D’Alembert’s functional equation on topological monoids. Publ. Math. Debrecen 75(1/2), 41–66 (2009)
Gajda Z.: A generalization of d’Alembert’s functional equation. Funkcial. Ekvac. 33(1), 69–77 (1990)
Kannappan P.: The functional equation f(xy) + f(xy −1) = 2f(x)f(y) for groups. Proc. Am. Math. Soc. 19, 69–74 (1968)
Kannappan P.: Functional Equations and Inequalities with Applications. Springer Monographs in Mathematics. Springer, New York (2009)
Nagy B.S.: A sine functional equation in Banach algebras. Publ. Math. Debrecen 24(1–2), 77–90 (1977)
Perkins, A.M., Sahoo, P.K.: On two functional equations with involution on groups related to sine and cosine functions. Aequationes Math. (2014). doi:10.1007/s00010-014-0309-z
Stetkær, H.: d’Alembert’s functional equation on groups. Recent developments in functional equations and inequalities, pp. 173–191, Banach Center Publ., vol. 99. Polish Acad. Sci. Inst. Math., Warsaw (2013)
Stetkær H.: Functional Equations on Groups. World Scientific Publishing Co, Singapore (2013)
Van Vleck E.B.: A functional equation for the sine. Ann. Math. Second Ser. 11(4), 161–165 (1910)
Vleck, E.B. Van: A functional equation for the sine. Additional note. Ann. Math. Second Ser. 13(1/4), 154 (1911–1912)
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We dedicate this paper to professor Roman Ger on the occasion of his 70th birthday
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Stetkær, H. Van Vleck’s functional equation for the sine. Aequat. Math. 90, 25–34 (2016). https://doi.org/10.1007/s00010-015-0349-z
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DOI: https://doi.org/10.1007/s00010-015-0349-z