Parseval-Rayleigh identities for graded Artinian Gorenstein algebras

TL;DR

This paper establishes Parseval-Rayleigh identities for graded Artinian Gorenstein algebras over fields of positive characteristic and applies these results to Stanley-Reisner rings of oriented simplicial spheres.

Contribution

It formulates and proves new Parseval-Rayleigh identities in the context of graded Artinian Gorenstein algebras, with applications to combinatorial algebraic topology.

Findings

Established Parseval-Rayleigh identities for a new class of algebras.

Provided an alternative proof for identities related to Stanley-Reisner rings.

Extended identities to algebras over fields of positive characteristic.

Abstract

We formulate and prove Parseval-Rayleigh identities for graded Artinian Gorenstein algebras over fields of positive characteristic. Specializing the general result, we provide an alternative proof of the Parseval-Rayleigh identities of generic Artinian reductions of Stanley-Reisner rings of oriented simplicial spheres.