Weighted discrete tori and weighted trigonometric sums
Shuofeng Huang, Chengjie Yu
TL;DR
This paper extends a known trigonometric summation formula by introducing weights, generalizing previous results by Grigor'yan, Lin, and Yau.
Contribution
It presents a new weighted summation formula for discrete tori, expanding the theoretical framework of trigonometric sums.
Findings
Derived a generalized weighted summation formula
Extended previous unweighted formulas to include weights
Potential applications in spectral graph theory and harmonic analysis
Abstract
In this paper, we obtain a weighted trigonometric summation formula which is an extension of the trigonometric summation formula by Grigor'yan, Lin and Yau \cite{GLY}.
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