Quadrature formula and zeros of para-orthogonal polynomials on the unit circle

By L. Golinski. 2002

78 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1cd64ab9bc2d41d1e33551991455c3e22dcb3894

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

In Computational Theory and Mathematics

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

In Numerical Analysis

1. Barry Simon
2. Alexander Pushnitski
3. David Damanik
4. Yoram Last

Citations in the corpus

• OPUC on one foot (2005, background): “rner. This implies that if β∈ ∂D, then Φ(β) N ≡ zΦN−1 − βΦ∗N −1 has all its zeros on ∂D since they are eigenvalues of a unitary matrix. The Φ(β) N are called paraorthogonal polynomials and studied in [31, 44, 37]. Dombrowski [20] proved that a Jacobi matrix with liminf an = 0 has no a.c. spectrum by”
• The Analytic Theory of Matrix Orthogonal Polynomials (2007, background): “sures on ∂D, they have a weak limit. By using limits, {ϕR j } ∞ j=0 are the right MOPUC for dµand they determine the proper Verblunsky coefficients. 3.8 Matrix POPUC Analogously to the scalar case (see [15, 100, 119, 172, 197]), given any unitary βin Ml, we define ϕR n (z;β) = zϕRn−1(z) −ϕ L,∗ n−1(z)β ”
• Two extensions of Lubinsky’s universality theorem (2008, background): “All our arguments extend with little change to finite gap OPUC and to zeros of paraorthogonal polynomials [3, 4, 11, 14, 32, 49].”
• FINE STRUCTURE OF THE ZEROS OF ORTHOGONAL POLYNOMIALS, I. A TALE OF TWO PICTURES (2004, unknown): “tions 8–13. We mention some examples in Section 13. 3. Stoiciu’s Resultson the Random Case Recall that given β∈ ∂Dand {Φn}∞ n=0, a set of orthogonal polynomials, the paraorthogonal polynomials (POPs) [18, 16] are defined by Φn(z;β) = zΦn−1(z) − β¯Φ∗ n−1(z) (3.1) They have all their zeros on ∂D(see, e”
• Fine Structure of the Zeros of Orthogonal Polynomials, IV. A Priori Bounds and Clock Behavior (2006, methodology): “sion of some bounds of Deift-Simon [8]. In Section 9, we discuss lower bounds on eigenvalue spacing. The methods in Sections 8 and 9 are borrowed from Erd¨os-Tur´an [9, 51], Nevai [34], and Golinskii [14], but we show how to localize them and squeeze out stronger results. In Section 10, we briefly di”
• The Christoffel-Darboux Kernel (2008, methodology): “The following theorem of Last–Simon [57], based on ideas of Golinskii [41], can be used on successive zeros (see [57] for the proof).”