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- W3204117395 abstract "Abstract The primary object of study is the “cosine-sine” functional equation f ( xy ) = f ( x ) g ( y )+ g ( x ) f ( y )+ h ( x ) h ( y ) for unknown functions f, g, h : S → ℂ, where S is a semigroup. The name refers to the fact that it contains both the sine and cosine addition laws. This equation has been solved on groups and on semigroups generated by their squares. Here we find the solutions on a larger class of semigroups and discuss the obstacles to finding a general solution for all semigroups. Examples are given to illustrate both the results and the obstacles. We also discuss the special case f ( xy ) = f ( x ) g ( y ) + g ( x ) f ( y ) − g ( x ) g ( y ) separately, since it has an independent direct solution on a general semigroup. We give the continuous solutions on topological semigroups for both equations." @default.
- W3204117395 created "2021-10-11" @default.
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- W3204117395 date "2021-10-05" @default.
- W3204117395 modified "2023-10-12" @default.
- W3204117395 title "The Cosine-Sine Functional Equation on Semigroups" @default.
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- W3204117395 doi "https://doi.org/10.2478/amsil-2021-0012" @default.
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