Asymptotics for Christoffel functions for general measures on the real line

By Vilmos Totik. 2000

124 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3a0c9d08a08515a40c0bf7a679ec89dbceaee272

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Doron S. Lubinsky
2. Barry Simon
3. Vilmos Totik
4. Eli Levin
5. András Kroó
6. Mihai Putinar
7. Igor Mezi'c
8. Milan Korda

In Mathematical Physics

1. Doron S. Lubinsky
2. Vilmos Totik
3. Barry Simon
4. Eli Levin
5. András Kroó
6. Mihai Putinar
7. Igor Mezi'c
8. Milan Korda

In Numerical Analysis

1. Doron S. Lubinsky
2. Barry Simon
3. Eli Levin
4. Mihai Putinar
5. Igor Mezi'c
6. Milan Korda
7. András Kroó

Citations in the corpus

• Universality and fine zero spacing on general sets (2009, methodology): “locally uniformly in O. In [ 19 ] the emphasis was on proving (8.1) a.e.”
• Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials (2013, background): “If supp[µ] consists of finitely many intervals, a sufficient condition for regularity, called the Erdős–Turán criterion, is that µ ′ > 0 a.e. in supp[µ].”
• Data-driven spectral analysis of the Koopman operator (2017, methodology): “Consult [40, 43] for the state of the art on this matter.”
• Universality limits in the bulk for arbitrary measures on compact sets (2008, background): “It was Vili Totik who rst observed that universality can be proved at Lebesgue points, rather than just points of continuity [25].”
• Christoffel functions on curves and domains (2009, background): “Thus, in a sense, the basis of the proof is the application of polynomial mappings, so it resembles the reasonings in [37] and [36].”
• Universality limits in the bulk for varying measures (2008, methodology): “Moreover, one can use the methods of [31], or perhaps in greater generality, those of [50], [51], to establish (d).”
• Orthogonal polynomials (2005, unknown): “For all the results below see Stahl–Totik [87] and the references therein.”
• The Analytic Theory of Matrix Orthogonal Polynomials (2007, unknown): “(5) Prove Conjecture 5.9 extending a result of Stahl–Totik [180] from OPRL to MOPRL.”
• The Christoffel-Darboux Kernel (2008, background): “The extension to general sets via polynomial mapping and approximation (see Section 18) is due to Totik [96].”
• A New Approach to Universality Limits Involving Orthogonal Polynomials (2007, methodology): “We could use existing results in [7], [9], [10], [15] to treat the case where x + a/n ∈ J , and add a proof for the case where this fails, but the amount of effort seems almost the same.”