Abstract

We investigate the existence and representation of transmutations, also known astransformation operators, for strings. Using measure theory and functional analytic methods weprove their existence and study their representation. We show that in general they are not closeto unity since their representation does not involve a Volterra operator but rather the eigenvalueparameter. We also obtain conditions under which the transmutation is either a bounded or acompact operator. Explicit examples show that they cannot be reduced to Volterra type operators.

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