2 citations · 5 across the 13 of their papers we have counts for
14 papers
Complex analytic theory of Sturm-Liouville operators with Schatten -class resolvents
Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill
We use the theory of entire functions of finite order to prove a universal spectral dependence of the blowup/decay rate of solutions of the Sturm-Liouville eigenvalue equation for…
-functions via contour integrals and universal sum rules
Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill
This work develops an analytic framework for the study of the -function associated with general sequences of complex numbers. We show that a contour integral representation, com…
Arctic curves of periodic dimer models and generalized discriminants
Mateusz Piorkowski
We compute the algebraic equation for arctic curves of the Aztec diamond with a doubly (quasi-)periodic weight structure and obtain similar results for certain models of the hexago…
The spectral -function for quasi-regular Sturm--Liouville operators
Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill
In this work we analyze the spectral -function associated with the self-adjoint extensions, , of quasi-regular Sturm--Liouville operators that are bounded from below. B…
Finer limit circle/limit point classification for Sturm-Liouville operators
Mateusz Piorkowski, Jonathan Stanfill
In this paper we introduce an index which we call the `regularization index' associated to the endpoints, , of no…
Wiener-Hopf factorizations and matrix-valued orthogonal polynomials
Arno B. J. Kuijlaars, Mateusz Piorkowski
We compare two methods for analysing periodic dimer models. These are the matrix-valued orthogonal polynomials approach due to Duits and one of the authors, and the Wiener-Hopf app…
The Jacobi operator on and its various -functions
Fritz Gesztesy, Lance L. Littlejohn, Mateusz Piorkowski +1
We offer a detailed treatment of spectral and Weyl-Titchmarsh-Kodaira theory for all self-adjoint Jacobi operator realizations of the differential expression \begin{align*} τ_{α,β}…
Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function
Percy Deift, Mateusz Piorkowski
We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure on . The asymp…
The Jacobi operator and its Donoghue -functions
Fritz Gesztesy, Mateusz Piorkowski, Jonathan Stanfill
In this paper we construct Donoghue -functions for the Jacobi differential operator in , associated to the differential expression \begi…
Donoghue -functions for singular Sturm--Liouville operators
Fritz Gesztesy, Lance L. Littlejohn, Roger Nichols +2
Let be a densely defined, closed, symmetric operator in the complex, separable Hilbert space with equal deficiency indices and denote by $\mathcal{N}_i = \ke…
A scalar Riemann-Hilbert problem on the torus: Applications to the KdV equation
Mateusz Piorkowski, Gerald Teschl
We take a closer look at the Riemann-Hilbert problem associated to one-gap solutions of the Korteweg-de Vries equation. To gain more insight, we reformulate it as a scalar Riemann-…
Riemann-Hilbert Theory without local Parametrix Problems: Applications to Orthogonal Polynomials
Mateusz Piorkowski
We study whether in the setting of the Deift-Zhou nonlinear steepest descent method one can avoid solving local parametrix problems explicitly, while still obtaining asymptotic res…
Parametrix problem for the Korteweg--de Vries equation with steplike initial data
Mateusz Piorkowski
In this paper we study the asymptotics of solutions to the Korteweg--de Vries equation with steplike initial data, which lead to shock waves in the region between the asymptoticall…
Asymptotics of KdV shock waves via the Riemann-Hilbert approach
Iryna Egorova, Mateusz Piorkowski, Gerald Teschl
This paper discusses some general aspects and techniques associated with the long-time asymptotics of steplike solutions of the Korteweg--de Vries (KdV) equation via vector Riemann…