Inverse spectral problems for Dirac-type operators with global delay on a star graph

We introduce Dirac-type operators with a global constant delay on a star graph consisting of m equal edges. For our introduced operators, we formulate an inverse spectral problem that is recovering the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except for a specific boundary vertex v0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{0}$$\end{document} (called the root). For simplicity, we restrict ourselves to the constant delay not less than the edge length of the graph. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained.