FINE STRUCTURE OF THE ZEROS OF ORTHOGONAL POLYNOMIALS, I. A TALE OF TWO PICTURES

By Barry Simon. 2004

72 citations recorded by the source corpus.

Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large n. Motivated by two plots, we look at the finer structure for the case of the Verblunsky coefficients and for what we call the BLS condition: αn = Cb^n + O ((bΔ)^n). In the former case, we describe the results of Stoiciu. In the latter case, we prove asymptotically equal spacing for the bulk of zeros.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/980e1b6cf93dce78a682aba749849f5a2ba54a4c

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In Applied Mathematics

1. Barry Simon
2. David Damanik
3. Doron S. Lubinsky
4. N. H. Bingham
5. Alexander Pushnitski
6. David Damanik
7. Vilmos Totik
8. Rowan Killip

In Mathematical Physics

1. Barry Simon
2. Doron S. Lubinsky
3. David Damanik
4. David Damanik
5. Alexander Pushnitski
6. Vilmos Totik

In Numerical Analysis

1. Barry Simon

Citations in the corpus

• The Christoffel-Darboux Kernel (2008, background): “Without knowing of Freud’s work, Simon, in a series of papers (one joint with Last) [82, 83, 84, 57], focused on this behavior, called it clock spacing, and proved it in a variety of situations (not using universality or the CD kernel).”