Jacobi matrices on trees

Volume 118 / 2010

Agnieszka M. Kazun, Ryszard Szwarc Colloquium Mathematicum 118 (2010), 465-497 MSC: Primary 47B36; Secondary 42C05. DOI: 10.4064/cm118-2-7

Abstract

Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always essentially selfadjoint independently of the growth of its coefficients. In case a tree has one origin and infinitely many ends, the essential selfadjointness is equivalent to that of an ordinary Jacobi matrix obtained by restriction to the so called radial functions. For nonselfadjoint matrices the defect spaces are described in terms of the Poisson kernel associated with the boundary of the tree.

Authors

  • Agnieszka M. KazunInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Ryszard SzwarcInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    and
    Institute of Mathematics and Computer Science
    University of Opole
    Oleska 48
    45-052 Opole, Poland
    e-mail

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