Generalized hyperbolic functions, circulant matrices and functional equations
نویسنده
چکیده
There is a contrast between the two sets of functional equations f0(x + y) = f0(x)f0(y) + f1(x)f1(y), f1(x + y) = f1(x)f0(y) + f0(x)f1(y), and f0(x − y) = f0(x)f0(y)− f1(x)f1(y), f1(x − y) = f1(x)f0(y)− f0(x)f1(y) satisfied by the even and odd components of a solution of f(x + y) = f(x)f(y). J. Schwaiger and, later, W. Förg-Rob and J. Schwaiger considered the extension of these ideas to the case where f is sum of n components. Here we shorten and simplify the statements and proofs of some of these results by a more systematic use of matrix notation.
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