Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Eichinger, Benjamin"'
We derive necessary and sufficient conditions for universality limits for orthogonal polynomials on the real line and related systems. One of our results is that the Christoffel-Darboux kernel has sine kernel asymptotics at a point $\xi$, with regula
Externí odkaz:
http://arxiv.org/abs/2409.18045
Autor:
Eichinger, Benjamin, Woracek, Harald
Homogeneous spaces are de Branges' Hilbert spaces of entire functions with the property that certain weighted rescaling transforms induce isometries of the space into itself. A classical example of a homogeneous space is the Paley-Wiener space of ent
Externí odkaz:
http://arxiv.org/abs/2407.04979
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
This article examines the asymptotic behavior of the Widom factors, denoted $\mathcal{W}_n$, for Chebyshev polynomials of finite unions of Jordan arcs. We prove that, in contrast to Widom's proposal, when dealing with a single smooth Jordan arc, $\ma
Externí odkaz:
http://arxiv.org/abs/2312.12992
Autor:
Eichinger, Benjamin
We prove asymptotics of the Christoffel function, $\lambda_L(\xi)$, of a continuum Schr\"odinger operator for points in the interior of the essential spectrum under some mild conditions on the spectral measure. It is shown that $L\lambda_L(\xi)$ has
Externí odkaz:
http://arxiv.org/abs/2204.05633
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 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
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
There is a vast theory of the asymptotic behavior of orthogonal polynomials with respect to a measure on $\mathbb{R}$ and its applications to Jacobi matrices. That theory has an obvious affine invariance and a very special role for $\infty$. We exten
Externí odkaz:
http://arxiv.org/abs/2008.11884