2016/01/23 by Piotr Budzyński, Zenon Jan Jabłoński, Budzynski, Piotr +5 · 2 citations
Computer Science · Mathematics · #44A60 (Secondary) #47B20 (Primary) #47B33 #47B37 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1601.06261
openalex publication_date 2016/01/23 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
A recent example of a non-hyponormal injective composition operator in an\nL2-space generating Stieltjes moment sequences, invented by three of the\npresent authors, was built over a non-locally finite directed tree. The main\ngoal of this paper is to solve the problem of whether there exists such an\noperator over a locally finite directed graph and, in the affirmative case, to\nfind the simplest possible graph with these properties (simplicity refers to\nlocal valency). The problem is solved affirmatively for the locally finite\ndirected graph mathscr G2,0, which consists of two branches and one loop.\nThe only simpler directed graph for which the problem remains unsolved consists\nof one branch and one loop. The consistency condition, the only efficient tool\nfor verifying subnormality of unbounded composition operators, is intensively\nstudied in the context of mathscr G2,0, which leads to a constructive\nmethod of solving the problem. The method itself is partly based on\ntransforming the Krein and the Friedrichs measures coming either from shifted\nAl-Salam-Carlitz q-polynomials or from a quartic birth and death process.\n