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**1 - 2**of**2**### ON PERIODIC WAVE FUNCTIONS OF SCHRÖDINGER OPERATORS ON CAYLEY TREES

"... Abstract. In the paper we define periodic wave functions for a (discrete) Schrödinger operator on a Cayley tree. This periodicity depends on a subgroup of a group repre-sentation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schrödinger operator un ..."

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Abstract. In the paper we define periodic wave functions for a (discrete) Schrödinger operator on a Cayley tree. This periodicity depends on a subgroup of a group repre-sentation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schrödinger operator under which there are periodic wave functions. For a normal subgroup of infinite index we describe a class of periodic wave functions. Mathematics Subject Classifications (2010). 82B26.