The integro‐differential operators of infinite order on the half line related to the Legendre operator

摘要

In this paper, we introduce certain integro‐differential operators of Legendre type of infinite order. Some properties of these operators are obtained. Moreover, we establish the necessary and sufficient conditions for a class of integro‐differential operators of infinite order being unitary on L2(1,∞)$$ {L}_2left(1,infty right) $$. Some classes of related integro‐differential equations are also considered.