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Cauchy Problem of the non-self-adjoint Gauss-Laguerre semigroups and uniform bounds of generalized Laguerre polynomials

open access: yes, 2016
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-self-
Patie, Pierre, Savov, Mladen
core  

Bounds for zeros of the Laguerre polynomials

open access: yesJournal of Approximation Theory, 2003
The author shows that the least and largest zeros \(x_1, x_n\) of the Laguerre polynomial \(L_n ^{(\alpha)}(x)\) satisfies \[ x_1 > s-r + {(s-r)^{2/3} \over 2r^{1/3}} \] \[ x_n < s+r + {(s+r)^{2/3} \over 2r^{1/3}} \] with \[ s=2n+ \alpha +1, \;r= \sqrt{4n^2 +(2n-1)(2 \alpha +2)} \] provided \(n\geq 7, \alpha \geq 8\).
openaire   +1 more source

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