Subharmonic addition to the Beurling-Malliavin multiplier theorem

2022/10/17 by Б. Н. Хабибуллин, Khabibullin, B. N., E. G. Kudasheva +1
Mathematics · #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2210.09406

Abstract

We prove a version of the Beurling-Malliavin multiplier theorem. This version is formulated here in a simplified form. Let u\not≡ -∞ and M\not≡ -∞ be a pair of subharmonic functions on the complex plane \mathbb C with positive parts u⁺:=sup\u,0\ and M⁺ such that type[u]:=\limsup_{z→ ∞} (u⁺(z))/(|z|)lt;+∞, type[M]lt;+∞, ∫_-∞^+∞(u⁺(x)+M⁺(x))/(1+x²)dxlt;+∞. If type[u]

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