2021/04/29 by Żwilla Fechner, Fechner, Żwilla, Eszter Gselmann +3
Mathematics · #39B72 #43A70 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Functional Equations Stability Results #Primary 39B52 #Secondary 43A45 #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2104.14322
openalex publication_date 2021/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we continue the discussion about relations between exponential polynomials and generalized moment generating functions on a commutative hypergroup. We are interested in the following problem: is it true that every finite dimensional variety is spanned by moment functions? Let m be an exponential on X. In our former paper we have proved that if the linear space of all m-sine functions in the variety of an m-exponential monomial is (at most) one dimensional, then this variety is spanned by moment functions generated by m. In this paper we show that this may happen also in cases where the m-sine functions span a more than one dimensional subspace in the variety. We recall the notion of a polynomial hypergroup in d variables, describe exponentials on it and give the characterization of the so called m-sine functions. Next we show that the Fourier algebra of a polynomial hypergroup in d variables is the polynomial ring in d variables. Finally, using Ehrenpreis--Palamodov Theorem we show that every exponential polynomial on the polynomial hypergroup in d variables is a linear combination of moment functions contained in its variety.