Zobrazeno 1 - 10
of 88
pro vyhledávání: '"Yuditskii, Peter"'
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
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
Publikováno v:
In Advances in Mathematics May 2024 444
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap quasiperio
Externí odkaz:
http://arxiv.org/abs/2011.05266
In spectral theory, $j$-monotonic families of $2\times 2$ matrix functions appear as transfer matrices of many one-dimensional operators. We present a general theory of such families, in the perspective of canonical systems in Arov gauge. This system
Externí odkaz:
http://arxiv.org/abs/2011.05261
We consider canonical systems and investigate the Szeg\H{o} class, which is defined via the finiteness of the associated entropy functional. Noting that the canonical system may be studied in a variety of gauges, we choose to work in the Arov gauge,
Externí odkaz:
http://arxiv.org/abs/1907.03267
Autor:
Yuditskii, Peter
We derive Fourier integral associated to the complex Martin function in the Denjoy domain of Widom type with the Direct Cauchy Theorem (DCT). As an application we study reflectionless Weyl-Titchmarsh functions in such domains, related to them canonic
Externí odkaz:
http://arxiv.org/abs/1812.00612
We establish precise spectral criteria for potential functions $V$ of reflectionless Schr\"odinger operators $L_V = -\partial_x^2 + V$ to admit solutions to the Korteweg de-Vries (KdV) hierarchy with $V$ as an initial value. More generally, our metho
Externí odkaz:
http://arxiv.org/abs/1802.00052
Publikováno v:
Duke Math. J. 168, no. 2 (2019), 325-349
We prove Szeg\H{o}-Widom asymptotics for the Chebyshev polynomials of a compact subset of $\mathbb{R}$ which is regular for potential theory and obeys the Parreau-Widom and DCT conditions.
Externí odkaz:
http://arxiv.org/abs/1709.06707
Autor:
Eichinger, Benjamin, Yuditskii, Peter
We raise a conjecture that asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due to Garabe
Externí odkaz:
http://arxiv.org/abs/1612.02949