Orthogonal Polynomials for Exponential Weights

By Eli Levin, Doron S. Lubinsky. 2001

280 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0b5bd224a18583a890040ea945ecdf5d1afa93a4

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Data-driven spectral analysis of the Koopman operator (2017, methodology): “al polynomials we refer to the ample eulogy of Geza Freud by Nevai [31], the more recent articles by Simon [39] and Totik [43] as well as the comprehensive books by Simon [40] and Levin and Lubinsky [22]. See also the seminal work of Wiener [45] for a predecessor of the methods used in this work. Fo”
Universality for eigenvalue correlations from the modified Jacobi unitary ensemble (2002, background): “We remark that, under various assumptions, asymptotic results on the interval of orthogonality have been established by many authors, see for example [4, 5, 14, 15, 21, 25, 26].”
Decomposition of Spaces of Distributions Induced by Hermite Expansions (2007, unknown): “We insert this in (4.4) and apply Lemma 4.7 and the maximal inequality (2.40) to obtain ‖f‖Fαqp ≤ ∥∥∥ ( ∞∑ j=0 (2jα|S∗j (·)|)q )1/q∥∥∥ p ≤ ∥∥∥ ( ∞∑ j=0 [ Ms ( 2jα ∑ ξ∈Xj |sξ||Rξ|−1/21Rξ)]q)1/q∥∥∥ p ≤ c‖{sη}‖fαqp .”
A Survey of Weighted Polynomial Approximation with Exponential Weights (2007, background): “See [57], [61], [85], [134], [136], [145], [163] for further discussion of restricted range inequalities.”
Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports (2006, methodology): “From this theorem and very well-known results for orthogonal polynomials associated with exponential weights, see for example [21], we deduce:”
Polynomial Frames: A Fast Tour (2004, background): “The theory of Freud polynomials is quite well developed [42, 73, 34].”
Universality limits in the bulk for varying measures (2008, methodology): “Here, to accord with [31], I is the (possibly unbounded) interval of orthogonality of W 2.”
Orthogonal polynomials (2005, unknown): “in [46] a theory was developed by Levin and Lubinsky that simultaneously includes far reaching generalizations of non-symmetric Freud, Erdős and Pollaczek weights such as (a) nonsymmetric Freud-type weights”