Summary
We solve the equationf(x + y)f(x − y) = P(f(x), f(y)) under various conditions on the unknown functionsf, P.
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References
Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York, 1966.
Aczél, J. andDhombres, J.,Functional equations in several variables. Cambridge Univ. Press, Cambridge, 1989.
Fuchs, L.,Infinite abelian groups, vol. I. Academic Press, New York, 1970.
Halter-Koch, F., Reich, L. andSchwaiger, J.,On products of additive functions. Aequationes Math.45 (1993), 83–88.
Perelli, A.-Zannier, U.,Su un'equazione funzionale legata agli omomorfismi di un gruppo in un corpo. Boll. Un. Mat. Ital. (6)5-B (1986), 235–245.
Reich, L. andSchwaiger, J.,On polynomials in additive and multiplicative functions. InFunctional equations: history, applications and theory (ed. J. Aczél). Reidel, Dordrecht, 1984, pp. 127–160.
Sinopoulos, P., The functional equation\(\left| {\begin{array}{*{20}c} {f(x - t)} & {g(x + t)} \\ {f(y - t)} & {g(y + t)} \\ \end{array} } \right| = h(t)\phi (x,y)\). Bull. Greek Math. Soc.28 (1987), part B, 29–42.
Sinopoulos, P.,Generalized sine equations, I. Aequationes Math.48 (1994), 171–193.
Sinopoulos, P.,Generalized sine equations, II. Aequationes Math.49 (1995), 122–152.
Székelyhidi, L.,Convolution type functional equations on topological abelian groups. World Scientific Publ., Singapore, 1991.
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Sinopoulos, P. Generalized sine equations, III. Aeq. Math. 51, 311–327 (1996). https://doi.org/10.1007/BF01833286
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DOI: https://doi.org/10.1007/BF01833286