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On AAA approximants on an interval to Nevanlinna-Pick functions and Pólya Frequency Series
Sergey A. Denisov, Maxim L. Yattselev
We study the connection between AAA (triple A) algorithm and multi-point Padé approximation when the approximated functions belong to either the Nevanlinna-Pick class or are Pólya…
Asymptotics of Polynomials Orthogonal on an Interval with Varying Weights
Sergey A. Denisov, Maxim L. Yattselev
We study strong asymptotics of orthogonal polynomials on an interval with varying weights, extending the framework of Totik's theorem on weighted orthogonal polynomials. Our result…
Pointwise behavior of SU(1,1) nonlinear Fourier transform
Sergey A. Denisov
We show that SU(1,1) NLFT can diverge pointwise for square-summable coefficients. As a consequence, we prove that the classical pointwise asymptotics of polynomials orthogonal on t…
Convergence of sparse square-summable NLFT
Sergey A. Denisov
We study the convergence of SU(1,1) and SU(2) nonlinear Fourier transform with sparse square-summable data. The asymptotics of the associated polynomials orthogonal on the unit cir…
The strong version of nonlinear Carleson conjecture fails
Sergey A. Denisov
In the context of the Dirac equation with square-summable potential, we study the Jost solutions and prove that the maximal function associated with the argument of the transmissio…
Strong Asymptotics of Multiple Orthogonal Polynomials for Angelesco Systems. Part I: Non-Marginal Directions
A. I. Aptekarev, S. A. Denisov, M. L. Yattselev
In this work, we establish strong asymptotics of multiple orthogonal polynomials of the second type for Angelesco systems with measures that satisfy Szegő conditions. We consider m…