The boundary control approach to the Titchmarsh-Weyl m-function

2025/05/29 by Avdonin, S. A., Mikhaylov, V. S., Rybkin, A. V. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.23332

Abstract

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A-amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m-function associated with the Schrödinger operator H=-∂ _x²+q( x) on L₂( 0,∞ ) with Dirichlet boundary condition at x=0.

Citations

• Equivalence of time-domain inverse problems and boundary spectral problems
• Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators
• A new approach to inverse spectral theory, I. Fundamental formalism
• A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure

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