SU\G(𝔸)/K·U

The functional equation 𝑓(𝑥𝑦)+𝑓(𝑥𝑦⁻¹)=2𝑓(𝑥)𝑓(𝑦) for groups

Pl. Kannappan

Type: Article

Publication Date: 1968-01-01

Citations: 89

DOI: https://doi.org/10.1090/s0002-9939-1968-0219936-1

Abstract

wheref is a complex-valued function on a group G, for all x, y in G. On the line this functional equation is obviously satisfied by the cosine function and may be called the cosine equation. Of course this equation has a meaning on any group. One obvious way to solve the functional equation (A) on any group is by means of a homomorphism of G, say g, into the multiplicative group of nonzero complex numbers, K. If g is such a homomorphism, then the function defined by

Locations

  • Proceedings of the American Mathematical Society - View - PDF

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+ PDF Chat On the functional equation 𝑓(𝑡)=𝑔(𝑡)-𝑔(2𝑡) 1962 Z. Ciesielski
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+ On the Functional Equation <i>f</i>(<i>x</i> + <i>y</i>) + <i>f</i>(<i>x</i> - <i>y</i>) = 2<i>f</i>(<i>x</i>)<i>f</i>(<i>y</i>) 1965 Pl. Kannappan
+ PDF Chat Continuous Solutions of the Functional Equation f<sup>n</sup>(x) = f(x) 1953 George M. Ewing
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