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Cauchy problem of the non-self-adjoint Gauss–Laguerre semigroups and uniform bounds for generalized Laguerre polynomials
We propose a new approach to construct the eigenvalue expansion in a weighted Hilbert space of the solution to the Cauchy problem associated to Gauss–Laguerre invariant Markov semigroups that we introduce. Their generators turn out to be natural non-selfadjoint and non-local generalizations of the Laguerre differential operator. Our methods rely …