5 citations · 11 across the 14 of their papers we have counts for
16 papers
Almost periodic solutions of the defocusing mKdV equation
Long Li, Milivoje Lukić
We study the Cauchy problem for the defocusing mKdV equation with almost periodic initial data. If the initial data corresponds to a reflectionless Dirac operator which satisfies c…
New universality classes associated to fractals
Benjamin Eichinger, Alexander Kheifets, Milivoje Lukić +1
The local behavior of zeros of orthogonal polynomials is determined by the local scaling behavior of Christoffel-Darboux (CD) kernels. All previously studied behaviors are describe…
Clock spacing for two-sided Jacobi matrices
Benjamin Eichinger, Milivoje Lukić, Giorgio Young
We study local eigenvalue spacing for finite truncations of a two-sided Jacobi matrix with two movable endpoints. In particular, we show that a suitable analog of clock spacing fol…
Almost Periodic Solutions of The Cubic Defocusing Nonlinear Schrödinger Equation
Jake Fillman, Long Li, Milivoje Lukić +1
This paper addresses the Cauchy problem for the cubic defocusing nonlinear Schrödinger equation (NLS) with almost periodic initial data. We prove that for small analytic quasiperio…
Spectral properties of Schrödinger operators with locally potentials
Milivoje Lukić, Selim Sukhtaiev, Xingya Wang
We study half-line Schrödinger operators with locally potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Las…
Limit-Periodic Dirac Operators with Thin Spectra
Benjamin Eichinger, Jake Fillman, Ethan Gwaltney +1
We prove that limit-periodic Dirac operators generically have spectra of zero Lebesgue measure and that a dense set of them have spectra of zero Hausdorff dimension. The proof comb…
The Deift Conjecture: A Program to Construct a Counterexample
David Damanik, Milivoje Lukić, Alexander Volberg +1
We describe a program to construct a counterexample to the Deift conjecture, that is, an almost periodic function whose evolution under the KdV equation is not almost periodic in t…
An approach to universality using Weyl m-functions
Benjamin Eichinger, Milivoje Lukić, Brian Simanek
We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at t…
Asymptotics of Chebyshev rational functions with respect to subsets of the real line
Benjamin Eichinger, Milivoje Lukić, Giorgio Young
There is a vast theory of Chebyshev and residual polynomials and their asymptotic behavior. The former ones maximize the leading coefficient and the latter ones maximize the point…
Stahl-Totik Regularity for Dirac Operators
Benjamin Eichinger, Ethan Gwaltney, Milivoje Lukić
We develop a theory of regularity for Dirac operators with uniformly locally square-integrable operator data. This is motivated by Stahl--Totik regularity for orthogonal polynomial…
Reflectionless canonical systems, II. Almost periodicity and character-automorphic Fourier transforms
Roman Bessonov, Milivoje Lukić, Peter Yuditskii
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes,…
Reflectionless canonical systems, I. Arov gauge and right limits
Roman Bessonov, Milivoje Lukić, Peter Yuditskii
In spectral theory, -monotonic families of matrix functions appear as transfer matrices of many one-dimensional operators. We present a general theory of such famili…
Orthogonal rational functions with real poles, root asymptotics, and GMP matrices
Benjamin Eichinger, Milivoje Lukić, Giorgio Young
There is a vast theory of the asymptotic behavior of orthogonal polynomials with respect to a measure on and its applications to Jacobi matrices. That theory has an ob…
Stahl--Totik regularity for continuum Schrödinger operators
Benjamin Eichinger, Milivoje Lukić
We develop a theory of regularity for continuum Schrödinger operators based on the Martin compactification of the complement of the essential spectrum. This theory is inspired by S…
Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows
Milivoje Lukić, Giorgio Young
We consider the Cauchy problem for the KdV hierarchy -- a family of integrable PDEs with a Lax pair representation involving one-dimensional Schrödinger operators -- under a local…
Ergodic Schrödinger Operators in the Infinite Measure Setting
Michael Boshernitzan, David Damanik, Jake Fillman +1
We develop the basic theory of ergodic Schrödinger operators, which is well known for ergodic probability measures, in the case of a base dynamics on an infinite measure space. Thi…