Journal
ADVANCES IN MATHEMATICS
Volume 333, Issue -, Pages 796-821Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2018.05.038
Keywords
Schrodinger equation; Dispersive estimates; Jacobi polynomials
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Funding
- Austrian Science Fund (FWF) [P26060]
- Austrian Science Fund (FWF) [P26060] Funding Source: Austrian Science Fund (FWF)
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The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrodinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that dispersive estimates for the Schrodinger equation associated with the generalized Laguerre operator are connected with Bernstein type inequalities for Jacobi polynomials. We use known uniform estimates for Jacobi polynomials to establish some new dispersive estimates. In turn, the optimal dispersive decay estimates lead to new Bernstein-type inequalities. (C) 2018 Elsevier Inc. All rights reserved.
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