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Functional Equations and Distribution Functions

Results in Mathematics, 1994
Let \(a \in (0,1)\), \(N \in \mathbb{N} \backslash \{1\}\) and \(- 1 = \beta_0 \leq \beta_1 \leq \dots \leq \beta_{N - 1} = 1\). Then the functional equation \[ f(x) = {1 \over N} \sum^{N - 1}_{k = 0} f \left( {x - \beta_k \over a} \right) \] has a unique bounded solution \(f : \mathbb{R} \to \mathbb{R}\) vanishing on \((- \infty, -1/(1 - a))\) and ...
Borwein, Jonathan M., Girgensohn, Roland
openaire   +1 more source

On Wilson’s functional equations

Aequationes mathematicae, 2014
This paper concerns mainly a variant of Wilson's functional equation. It is shown that the solutions can be expressed in terms of characters, additive functions and matrix-elements of irreducible 2-dimensional representations of the underlying group. So the theory is part of the harmonic analysis on groups.
Ebanks, Bruce, Stetkaer, Henrik
openaire   +3 more sources

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