Reflectionless canonical systems, II. Almost periodicity and character-automorphic Fourier transforms

被引：0

作者：

Bessonov, Roman ^{[1
,2
]}

Lukic, Milivoje ^{[3
]}

Yuditskii, Peter ^{[4
]}

机构：

[1] St Petersburg State Univ, Univ Skaya Nab 7-9, St Petersburg 199034, Russia

[2] Russian Acad Sci, Steklov Math Inst, St Petersburg Dept, Fontanka 27, St Petersburg 191023, Russia

[3] Rice Univ, Dept Math, MS 136, Houston, TX 77251 USA

[4] Johannes Kepler Univ Linz, Abt Dynam Syst & Approximationstheorie, A-4040 Linz, Austria

来源：

ADVANCES IN MATHEMATICS | 2024年 / 444卷

基金：

奥地利科学基金会; 俄罗斯科学基金会;

关键词：

Almost periodicity; Reflectionless; Widom domain; Canonical system; Character-automorphic Hardy space; ABSOLUTELY CONTINUOUS-SPECTRUM; SCHRODINGER-OPERATORS; APPROXIMATION; MATRICES; THEOREM;

D O I：

10.1016/j.aim.2024.109636

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap quasiperiodic (algebro-geometric) solutions of stationary integrable hierarchies. Instead of theta functions on a compact Riemann surface, the construction is based on reproducing kernels of character-automorphic Hardy spaces in Widom domains with respect to Martin measure. We also construct unitary character-automorphic Fourier transforms which generalize the Paley-Wiener theorem. Finally, we find the correct notion of almost periodicity which holds for canonical system parameters in Arov gauge, and we prove generically optimal results for almost periodicity for Potapov-de Branges gauge, and Dirac operators. (c) 2024 Elsevier Inc. All rights reserved.

引用

页数：82