HOLOMORPHIC SOLUTIONS TO LINEAR q-DIFFERENCE EQUATIONS IN A BANACH SPACE

摘要

We prove the existence and uniqueness of a holomorphic solution to a linear q-difference equation for a closed operator with not necessarily dense domain in a Banach space. We consider holomorphic solutions in a neighborhood of zero in the case |q| < 1 and integer-valued solutions in the case |q| > 1. We obtain the solutions in an explicit form.