Direct spectral problems for Paley-Wiener canonical systems

Ashley R. Zhang

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arXiv · 2505.00669

Direct spectral problems for Paley-Wiener canonical systems

Ashley R. Zhang

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Abstract

This note focuses on the direct spectral problem for canonical Hamiltonian systems on the half-line $\mathbb{R}_+$. Truncated Toeplitz operators have been effectively used to solve the inverse spectral problem when the spectral measure is a locally finite periodic measure (see \cite{MP}). Here, we reverse the inverse problem algorithm to solve the direct spectral problem for step-function Hamiltonians. For a non-step-function Hamiltonian, we consider its step-function approximations and their corresponding spectral measures, and show that these spectral measures converge to the spectral measure of the original Hamiltonian.

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BibTeX RIS

Ashley R. Zhang. 2025-05-01. Direct spectral problems for Paley-Wiener canonical systems. https://arxiv.org/abs/2505.00669

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