The addition formula for theta functions |
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Authors: | Mario Bonk |
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Affiliation: | (1) Institut für Analysis, Techn. Universität Braunschweig, Pockelsstraße 14, D-38106 Braunschweig, Germany |
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Abstract: | Summary In this paper we solve the functional equationx(u + v)(u – v) = f1(u)g1(v) + f2(u)g2(v) under the assumption thatx, , f1, f2, g1, g2 are complex-valued functions onRn,n N arbitrary, and 0 and 0 are continuous. Our main result shows that, apart from degeneracy and some obvious modifications, theta functions of one complex variable are the only continuous solutions of this functional equation. |
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Keywords: | Primary 39B32 Secondary 33E05 |
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