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Cauchy problem of the non-self-adjoint Gauss–Laguerre semigroups and uniform bounds for generalized Laguerre polynomials
2017
Journal of Spectral Theory
We propose a new approach to construct an eigenvalue expansions in a weighted Hilbert space of the solution to the Cauchy problem associated to the so-called Gauss-Laguerre contraction semigroups, whose generators turns out to be a natural non-self-adjoint and nonlocal generalization of the Laguerre differential operators. Our methods rely on an intertwining relationship that we establish between this semigroup and the one of the classical Laguerre semigroup, combined with techniques based on
doi:10.4171/jst/178
fatcat:npppws2dsbbgbjqwpj56ecu33a