Poisson summation formulas: A new approach

2025/06/18 by Triebel, Hans
#42B35 #46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.15580

Abstract

The paper deals with a new approach to Poisson summation formulas in the context of function spaces on ℝⁿ.

Citations

• A Complete Classification of Fourier Summation Formulas on the real line
• A classification of Fourier summation formulas and crystalline measures
• Mapping properties of Fourier transforms, revisited
• A note on Hausdorff-Young inequalities in function spaces

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• Poisson summation formulas involving the sum-of-squares function
• A refined Poisson summation formula for certain Braverman-Kazhdan spaces
• Poisson-Newton formulas and Dirichlet series
• Some applications of the Poisson summation formula