2022/10/31 by Sergey Buterin, Buterin, Sergey · 5 citations
Mathematics · #34A55 34K29 34B45 #Advanced Mathematical Physics Problems #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2210.17266
openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves \it global delay parameter. Differential operators on graphs model various processes in many areas of science and technology. Although a vast majority of studies in this direction concern purely differential operators on graphs (often referred to as quantum graphs), recently there also appeared some considerations of nonlocal operators on star-type graphs. In particular, there belong functional-differential operators with constant delays but in a \it locally nonlocal version. The latter means that each edge of the graph has its own delay parameter, which does not affect any other edge. In this paper, we introduce \it globally nonlocal operators that are expected to be more natural for modelling nonlocal processes on graphs. We also extend this idea to arbitrary trees, which opens a wide area of further research. Another goal of the paper is to study inverse spectral problems for operators with global delay in one illustrative case by addressing a wide range of questions including uniqueness, characterization of the spectral data as well as the uniform stability.