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Generalized hyperbolic functions, circulant matrices and functional equations | Martin E. Muldoon
; | Date: |
27 Oct 1999 | Subject: | Classical Analysis and ODEs; Rings and Algebras MSC-class: 39B30, 15A57 | math.CA math.RA | Abstract: | There is a contrast between the two sets of functional equations f_0(x+y) = f_0(x)f_0(y) + f_1(x)f_1(y), f_1(x+y) = f_1(x)f_0(y) + f_0(x)f_1(y), and f_0(x-y) = f_0(x)f_0(y) - f_1(x)f_1(y), f_1(x-y) = f_1(x)f_0(y) - f_0(x)f_1(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. | Source: | arXiv, math.CA/9910143 | Services: | Forum | Review | PDF | Favorites |
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