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Search: All articles in the CMB digital archive with keyword functional equations

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1. CMB 2011 (vol 56 pp. 218)

Yang, Dilian
 Functional Equations and Fourier Analysis By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations - the d'Alembert equation, the Wilson equation, and the d'Alembert long equation - on compact groups. Keywords:functional equations, Fourier analysis, representation of compact groupsCategories:39B52, 22C05, 43A30

2. CMB 2011 (vol 55 pp. 60)

Coons, Michael
 Extension of Some Theorems of W. Schwarz In this paper, we prove that a non--zero power series $F(z)\in\mathbb{C} [\mkern-3mu[ z]\mkern-3mu]$ satisfying $$F(z^d)=F(z)+\frac{A(z)}{B(z)},$$ where $d\geq 2$, $A(z),B(z)\in\mathbb{C}[z]$ with $A(z)\neq 0$ and $\deg A(z),\deg B(z) Keywords:functional equations, transcendence, power seriesCategories:11B37, 11J81 3. CMB 2005 (vol 48 pp. 505) Bouikhalene, Belaid  On the Generalized d'Alembert's and Wilson's Functional Equations on a Compact group Let$G$be a compact group. Let$\sigma$be a continuous involution of$G$. In this paper, we are concerned by the following functional equation $$\int_{G}f(xtyt^{-1})\,dt+\int_{G}f(xt\sigma(y)t^{-1})\,dt=2g(x)h(y), \quad x, y \in G,$$ where$f, g, h \colonG \mapsto \mathbb{C}$, to be determined, are complex continuous functions on$G$such that$f$is central. This equation generalizes d'Alembert's and Wilson's functional equations. We show that the solutions are expressed by means of characters of irreducible, continuous and unitary representations of the group$G\$. Keywords:Compact groups, Functional equations, Central functions, Lie, groups, Invariant differential operators.Categories:39B32, 39B42, 22D10, 22D12, 22D15