Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups William Thomas Allison often referred to as birth

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Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups William Thomas Allison often referred to as birthWe provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non self adjoint and non local Markov operators which appear in limit theorems for positive valued Markov processes. We show that this class is in bijection with a subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the framework of perturbation theory, is based on an in depth