TL;DR
This paper extends the Poisson summation formula to higher dimensions using a trace formula derived from Von-Neumann's ergodic theorem, and constructs a family of crystalline measures with complex coefficients.
Contribution
It introduces a novel trace formula for unitary matrix families and constructs complex crystalline measures, expanding the mathematical tools in harmonic analysis.
Findings
Derived a trace formula from Von-Neumann's ergodic theorem.
Extended Poisson summation formula to higher dimensions.
Constructed a new family of crystalline measures with complex coefficients.
Abstract
We take the trace of Von-Neumann's ergodic theorem and get a trace formula of a unitary matrix family. It is an extension of Poisson summation formula in higher dimension. We also construct a family of crystalline measure with complex coefficient.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms