A remark on the Beurling-Malliavin theorem in several variables

2025/12/08 by Bergman, Alex
Mathematics · #30H10 #32Cxx #42B10 #42B30 #42B35 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.2512.07271

openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

Abstract

We use a lifting trick to show that the Beurling-Malliavin multiplier theorem extends to radial functions in several variables in a straightforward way. This simplifies an argument of Vasilyev and also answers a question of Vasilyev on the Cartwright version of the theorem.

Citations

• The Beurling and Malliavin Theorem in Several Dimensions
• Fractal uncertainty in higher dimensions
• Oscillation of Fourier Integrals with a spectral gap

Related

• The Beurling and Malliavin Theorem in Several Dimensions
• The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces
• Subharmonic addition to the Beurling-Malliavin multiplier theorem
• A Note on multipliers between model spaces
• On the connection between the Beurling-Malliavin density and the asymptotic density