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- Title
On certain generalizations of the Levi-Civita and Wilson functional equations.
- Authors
Almira, J.; Shulman, E.
- Abstract
We study the functional equation with $$x,y\in \mathbb {R}^d$$ and $$b_i,c_i\in {GL}(d,\mathbb {R})$$ , both in the classical context of continuous complex-valued functions and in the framework of complex-valued Schwartz distributions, where these equations are properly introduced in two different ways. The solution sets are, typically, exponential polynomials and, in some particular cases, related to the so called characterization problem of the normal distribution in Probability Theory, they reduce to ordinary polynomials.
- Subjects
THEORY of distributions (Functional analysis); SCHWARTZ distributions; FUNCTIONAL equations; MATHEMATICAL analysis; MODERN geometry
- Publication
Aequationes Mathematicae, 2017, Vol 91, Issue 5, p921
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-017-0489-4