On local non-tangential growth of the resolvent of a banded Toeplitz operator

2025/05/31 by Leonid Golinskiĭ, Golinskii, L., S. Kupin +1
Mathematics · #47G10 #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 47B35 #Secondary: 30H10 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.00584

openalex publication_date 2025/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the growth of the resolvent of a Hardy--Toeplitz operator T_b with a Laurent polynomial symbol (i.e., the matrix T_b is banded), at the neighborhood of a point w₀∈∂(σ(T_b)) on the boundary of its spectrum. We show that such growth is inverse linear in some non-tangential domains at the vertex w₀, provided that w₀ does not belong to a certain finite set on the complex plane.

Citations

• On the growth of resolvent of Toeplitz operators

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