A potpourri of algebraic properties of the ring of periodic distributions

2017/04/05 by Amol Sasane, Sasane, Amol
Mathematics · #Rings, Modules, and Algebras #Meromorphic and Entire Functions #Advanced Topics in Algebra

paper · doi:10.48550/arxiv.1704.01403

Abstract

The set of periodic distributions, with usual addition and convolution, forms a ring, which is isomorphic, via taking a Fourier series expansion, to the ring S'(ℤ^d) of sequences of at most polynomial growth with termwise operations. In this article, we establish several algebraic properties of these rings.

Related

• Coherence of the ring of periodic distributions
• Ideals in the convolution algebra of periodic distributions
• On the Bezout equation in the ring of periodic distributions
• The Collatz map analogue in polynomial rings and in completions
• On the product of periodic distributions. Product in shift-invariant spaces