Measures and para orthogonal polynomials on the unit circle

By Leandro Moral, María José Cantero Medina, Luis Velázquez Campoy. 2002

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Citations in the corpus

Minimal representations of unitary operators and orthogonal polynomials on the unit circle (2004, methodology): “ µt N , the sums run from 1 to Nand α N = β. The particular case of uniform rotations of the Schur parameters is specially interesting. It has been previously considered in [15] and by the authors in [4, 5, 6]. Corollary 5.6. Let a ∈ Dℵ0, u∈ T and α:I→ R diﬀerentiable. If a n(t) = a neiα(t) for n∈ N”
Fine Structure of the Zeros of Orthogonal Polynomials, IV. A Priori Bounds and Clock Behavior (2006, background): “Thus, the zeros of ˜ϕn lie on ∂D; indeed, they are the zeros of a ﬁnite unitary matrix (see Theorem 8.2.7 of [39]). Zeros of POPUC are discussed extensively in Golinskii [14], Cantero-MoralVel´azquez [3, 4], Simon [46], and Wong [55]. As explained in Section 10.8 of [40], there is an OPUC analog of ”
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].”
The Analytic Theory of Matrix Orthogonal Polynomials (2007, unknown): “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 ”
Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle (2006, methodology): “ will consider a sequence {βn}∞ n=1 ∈ ∂D and Φ˜ n(z) = Φn(z,dµ;βn) (1.4) POPUC were introduced at least as early as Jones, Nj˚astad, and Thron [6]. About ﬁve years ago, Cantero, Moral, and Vel´azquez [1] and Golinskii [5] realized that zeros of POPUC shared many properties of zeros of OPRL and indep”