arXiv subjects

J. S. Geronimo

Publications and source records attributed to J. S. Geronimo.

4 recordsLinked to original sources

arXiv2016

High order recurrence relation, Hermite-Padé approximation, and Nikishin systems

The study of sequences of polynomials satisfying high order recurrence relations is connected with the asymptotic behavior of multiple orthogonal polynomials, the convergence properties of type II Hermite-Padé approximation, and eigenvalue distribution of banded Toeplitz matrices. We present some results for the case of recurrences with constant coefficients which match what is known for the Chebyshev polynomials of the first kind. In particular, under appropriate assumptions, we show that the sequence of polynomials satisfies multiple orthogonality relations with respect to a Nikishin system of measures.

math.CV↗

arXiv2014

Measures for orthogonal polynomials with unbounded recurrence coefficients

Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are asymptotics for the polynomials.

math.CA↗

arXiv2005

On Extensions of a Theorem of Baxter

We combine the Riemann-Hilbert approach with the techniques of Banach algebras to obtain an extension of Baxter's Theorem for polynomials orthogonal on the unit circle. This is accomplished by using the link between the negative Fourier coefficients of the scattering function and the coefficients in the recurrence formula satisfied by these polynomials.

math.CA↗

arXiv2000

On Certain Two Dimensional Integrals that Appear In Conformal Field Theory

In a first part, we generalize a theorem for an holomorphic $\times $ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear combination of holomorphic times holomorphic generalized hypergeometric functions. The specific case $p=3$ is relevant to determine the triple Pomeron vertex in QCD.

math-ph↗