Two extensions of Lubinsky’s universality theorem

By Barry Simon. 2008

83 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aa789a96ab107dc97eacd318b2183f39e1aa126d

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. András Kroó
5. L. Erdős
6. David Damanik
7. Eli Levin
8. Alexander Pushnitski

In Computational Theory and Mathematics

1. Doron S. Lubinsky
2. Vilmos Totik
3. András Kroó
4. Barry Simon
5. David Damanik

In Mathematical Physics

1. Doron S. Lubinsky
2. Vilmos Totik
3. Barry Simon
4. András Kroó
5. L. Erdős
6. David Damanik
7. Eli Levin
8. Horng-Tzer Yau

Citations in the corpus

• Universality limits in the bulk for arbitrary measures on compact sets (2008, background): “The universality limit (1.4) was established uniformly for 2 J and a; b in compact subsets of the real line.”
• The Christoffel-Darboux Kernel (2008, methodology): “(x)u n (19.4) For x ∈ eint, un and ¯un are linearly independent, and so one can write p·−1 in terms of u· and ¯u·. Using ρ e(x) = 1 pπ dθ dx (19.5) one can prove (19.1) and (19.2). The details are in [87, 89]. 20. Lubinsky’s Inequality and Bulk Universality Lubinsky [60] found a powerful tool for go”
• Christoffel functions on curves and domains (2009, background): “also [4], [38] and particularly [31], where the importance of Christoffel functions regarding off diagonal behavior of the reproducing kernel was emphasized).”
• The Analytic Theory of Matrix Orthogonal Polynomials (2007, unknown): “ terms of expectations in any fixed vector. We state this explicitly since we will need it in Section 5.4, but we note that the more detailed results of M´at´e–Nevai–Totik [147], Lubinsky [141], Simon [173], and Totik [189] also extend. 2.9 Zeros We next look at zeros of det(PL n (z)), which we will ”
• Universality limits in the bulk for varying measures (2008, unknown): “Then (5.6) ` 1X j=k+1 n (tjn) e Btjn Z t`n tkn e Btd n (t) X̀ j=k n (tjn) e Btjn :”
• Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials (2013, background): “For the case of compactly supported µ that are regular and satisfy (1.2), Totik [18] showed that universality holds for a.e. x ∈ I.”