126 citations · 370 across the 18 of their papers we have counts for
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A CMV connection between orthogonal polynomials on the unit circle and the real line
M. J. Cantero, F. Marcellán, L. Moral +1
M. Derevyagin, L. Vinet and A. Zhedanov introduced in Constr. Approx. 36 (2012) 513-535 a new connection between orthogonal polynomials on the unit circle and the real line. It map…
The CMV bispectral problem
F. A. Grünbaum, L. Velázquez
A classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator. We settle a…
Darboux transformations for CMV matrices
M. J. Cantero, F. Marcellán, L. Moral +1
We develop a theory of Darboux transformations for CMV matrices, canonical representations of the unitary operators. In perfect analogy with their self-adjoint version -- the Darbo…
A quantum dynamical approach to matrix Khrushchev's formulas
C. Cedzich, F. A. Grünbaum, L. Velázquez +2
Khrushchev's formula is the cornerstone of the so called Khrushchev theory, a body of results which has revolutionized the theory of orthogonal polynomials on the unit circle. This…
Minimal representations of unitary operators and orthogonal polynomials on the unit circle
M. J. Cantero, L. Moral, L. Velazquez
In this paper we prove that the simplest band representations of unitary operators on a Hilbert space are five-diagonal. Orthogonal polynomials on the unit circle play an essential…