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pro vyhledávání: '"Treil, Sergei"'
We show that the famous matrix $A_2$ conjecture is false: the norm of the Hilbert Transform in the space $L^2(W)$ with matrix weight $W$ is estimated below by $C[W]_{{A}_2}^{3/2}$.
Comment: 46 pages, 5 figures
Comment: 46 pages, 5 figures
Externí odkaz:
http://arxiv.org/abs/2402.06961
We consider an inverse spectral problem for a class of non-compact Hankel operators $H$ such that the modulus of $H$ (restricted onto the orthogonal complement to its kernel) has simple spectrum. Similarly to the case of compact operators, we prove a
Externí odkaz:
http://arxiv.org/abs/2211.00965
Autor:
Liang, Zhehui, Treil, Sergei
We study the inverse problem for the Hankel operators in the general case. Following the work of G\'erard--Grellier, the spectral data is obtained from the pair of Hankel operators $\Gamma$ and $\Gamma S$, where $S$ is the shift operator. The theory
Externí odkaz:
http://arxiv.org/abs/2204.00115
Autor:
Liang, Zhehui, Treil, Sergei
We present an alternative proof of the result by P. Gerard and S. Grellier, stating that given two real sequences $(\lambda_n)_{n=1}^\infty$, $(\mu_n)_{n=1}^\infty$ satisfying the intertwining relations \[ |\lambda_1| > |\mu_1| > |\lambda_2| > |\mu_2
Externí odkaz:
http://arxiv.org/abs/2203.10650
Consider a tensor product of simple dyadic shifts defined below. We prove here that for dyadic bi-parameter repeated commutator its norm can be estimated from below by Chang-Fefferman $BMO$ norm pertinent to its symbol. See Theorems in Section 8 at t
Externí odkaz:
http://arxiv.org/abs/2101.00763
Let $\bfT$ is a certain tensor product of simple dyadic shifts defined below. We prove here that for dyadic bi-parameter commutator the following equivalence holds $ \|\bfT b-b \bfT \| \asymp \|b\|_{bmo^d}$. This result is well-known for many types o
Externí odkaz:
http://arxiv.org/abs/2012.05376
Autor:
Treil, Sergei, Liaw, Constanze
Publikováno v:
Algebra i Analiz, 2022, Volume 34, Issue 3, Pages 232-251
We consider contractive operators $T$ that are trace class perturbations of a unitary operator $U$. We prove that the dimension functions of the absolutely continuous spectrum of $T$, $T^*$ and of $U$ coincide. In particular, if $U$ has a purely sing
Externí odkaz:
http://arxiv.org/abs/2010.07908
Publikováno v:
International Mathematics Research Notices, Volume 2022, Issue 5, March 2022, Pages 3297-3307
The classical Aronszajn-Donoghue theorem states that for a rank one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple dire
Externí odkaz:
http://arxiv.org/abs/2005.05797
Publikováno v:
J. Funct. Anal. 280, iss. 3 (2021), 108830
This paper deals with families of matrix-valued Aleksandrov--Clark measures $\{\boldsymbol{\mu}^\alpha\}_{\alpha\in\mathcal{U}(n)}$, corresponding to purely contractive $n\times n$ matrix functions $b$ on the unit disc of the complex plane. We do not
Externí odkaz:
http://arxiv.org/abs/2005.02897
In this paper we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of
Externí odkaz:
http://arxiv.org/abs/2001.11182