Jacobi matrices on trees

• Autorzy: Agnieszka M. Kazun , Ryszard Szwarc
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42C05: Orthogonal functions and polynomials, general theory
• 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 465-497

Daty

wydano

2010

Twórcy

autor

Agnieszka M. Kazun

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Ryszard Szwarc

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
• Institute of Mathematics and Computer Science, University of Opole, Oleska 48, 45-052 Opole, Poland

Identyfikatory

DOI

10.4064/cm118-2-7