Point spectrum on a quasihomogeneous tree

K. Aomoto

Vol. 147 (1991), No. 2, 231–242

DOI: 10.2140/pjm.1991.147.231

Abstract

By using the algebraicity of the Green kernel it is shown that a linear operator of nearest neighbour type on a quasi homogeneous tree i.e. a tree admitting of a group of automorphism with finite quotient has no point spectrum on the space of square summable functions, provided the tree has a regular property and that the operator is invariant under the group of automorphism.

Mathematical Subject Classification 2000

Primary: 47B39

Secondary: 05C05, 47A10, 58F19

Milestones

Received: 17 April 1989

Revised: 18 January 1990

Published: 1 February 1991