1. On certain generalizations of the Levi-Civita and Wilson functional equations
- Author
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Almira, J. M. and Shulman, E. V.
- Subjects
Mathematics - Classical Analysis and ODEs ,43B45, 39A70, 39B52 - Abstract
We study the functional equation \[ \sum_{i=1}^mf_i(b_ix+c_iy)= \sum_{k=1}^nu_k(y)v_k(x) \] 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 so called characterization problem of the normal distribution in Probability Theory, they reduce to ordinary polynomials., Comment: 11 pages, submitted to a Journal; This is a re-doing of part of version v1. The results not included here will be send in another paper by J. M. Almira
- Published
- 2016