Zobrazeno 1 - 10
of 91
pro vyhledávání: '"Lukić, Milivoje"'
In general, point spectrum of an almost periodic Jacobi matrix can depend on the element of the hull. In this paper, we study the hull of the limit-periodic Jacobi matrix corresponding to the equilibrium measure of the Julia set of the polynomial $z^
Externí odkaz:
http://arxiv.org/abs/2405.19470
Autor:
Lukić, Milivoje, Wang, Xingya
We study Jost solutions of Schr\"odinger operators with potentials which decay with respect to a local $H^{-1}$ Sobolev norm; in particular, we generalize to this setting the results of Christ--Kiselev for potentials between the integrable and square
Externí odkaz:
http://arxiv.org/abs/2405.17715
We study half-line Schr\"odinger operators with locally $H^{-1}$ potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last--Simon-type description of the absolutely continuous spectrum and
Externí odkaz:
http://arxiv.org/abs/2206.07079
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 combines ideas of Avila from a Schr\"odinger setting with a new commutatio
Externí odkaz:
http://arxiv.org/abs/2203.12650
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 time. The approach is based on a dichotomy found by Volberg and Yuditsk
Externí odkaz:
http://arxiv.org/abs/2111.09345
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 the point. We show that bulk universality of the Christoffel-Darboux ke
Externí odkaz:
http://arxiv.org/abs/2108.01629
Publikováno v:
In Advances in Mathematics May 2024 444
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 evaluation with respect to an $L^\infty$ norm. We study Chebyshev and
Externí odkaz:
http://arxiv.org/abs/2101.01744
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 polynomials and by recent developments for continuum Schr\"odinger operators, bu
Externí odkaz:
http://arxiv.org/abs/2012.12889