Jacobi matrices on trees

Agnieszka M. Kazun, and Ryszard Szwarc. "Jacobi matrices on trees." Colloquium Mathematicae 118.2 (2010): 465-497. <http://eudml.org/doc/283746>.

@article{AgnieszkaM2010,
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.},
author = {Agnieszka M. Kazun, Ryszard Szwarc},
journal = {Colloquium Mathematicae},
keywords = {Jacobi matrices; symmetric and selfadjoint operators; orthogonal polynomials},
language = {eng},
number = {2},
pages = {465-497},
title = {Jacobi matrices on trees},
url = {http://eudml.org/doc/283746},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Agnieszka M. Kazun
AU - Ryszard Szwarc
TI - Jacobi matrices on trees
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 465
EP - 497
AB - 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.
LA - eng
KW - Jacobi matrices; symmetric and selfadjoint operators; orthogonal polynomials
UR - http://eudml.org/doc/283746
ER -