arXiv 1007.54122010-07math.FAmath-phmath.MPmath.SP

Sharp spectral estimates for periodic matrix-valued Jacobi operators

Anton A. Kutsenko

备注：: 3 pages

英文摘要：

For the periodic matrix-valued Jacobi operator $J$ we obtain the estimate of the Lebesgue measure of the spectrum $|\s(J)|\le4 \min_n\Tr(a_na_n^*)^\frac12$, where $a_n$ are off-diagonal elements of $J$. Moreover estimates of width of spectral bands are obtained.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Vector-valued L_p convergence of orthogonal series and Lagrange interpolation

We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of $L_p$-functions in terms of Jacobi polynomials and consider the question of unconditional convergence. The notion of type $p$ with respect to orthonormal systems leads to some characterizations of Hilbert spaces. It is also shown that various vector-valued Jacobi means are equivalent.

1992-08-13math.FA

Jacobi weights, fractional integration, and sharp Ulyanov inequalities

We consider functions L_p-integrable with Jacobi weights on [-1,1] and prove Hardy--Littlewood type inequalities for fractional integrals. As applications, we obtain the sharp (L_p, L_q) Ulyanov-type inequalities for the Ditzian--Totik moduli of smoothness and the K-functionals of fractional order.

2016-01-05math.FA

$L^q$-valued Burkholder-Rosenthal inequalities and sharp estimates for stochastic integrals

We prove sharp maximal inequalities for $L^q$-valued stochastic integrals with respect to any Hilbert space-valued local martingale. Our proof relies on new Burkholder-Rosenthal type inequalities for martingales taking values in an $L^q$-space.

2017-07-21math.FAmath.PR

Inequalities for the eigenvalues of non-selfadjoint Jacobi operators

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on determinants of operators and on complex function theory, extending and sharpening earlier work of Borichev, Golinskii and Kupin.

2009-01-13math.FAmath.SP

Sharp extensions and algebraic properties for solution families of vector-valued differential equations

In this paper we show the unexpected property that extension from local to global without loss of regularity holds for the solutions of a wide class of vector-valued differential equations, in particular for the class of fractional abstract Cauchy problems in the subdiffusive case. The main technique is the use of the algebraic structure of these solutions, which are defined by new versions of functional equations defining solution families of bounded operators. The convolution product and the double Laplace transform for functions of two variables are useful tools which we apply also to exten…

2015-05-12math.FA

Sharp rigidity estimates for incompatible fields as consequence of the Bourgain Brezis div-curl result

In this note we show that a sharp rigidity estimate and a sharp Korn's inequality for matrix-valued fields whose incompatibility is a bounded measure can be obtained as a consequence of a Hodge decomposition with critical integrability due to Bourgain and Brezis.

2020-09-17math-phmath.APmath.FA

更多相关论文收起更多论文

稀疏控制蕴含向量值稀疏控制

Sparse domination implies vector-valued sparse domination

本文证明多线性算子的标量值稀疏控制蕴含向量值稀疏控制，引入UMD条件的多线性类比，从而直接获得精确的向量值加权界，并应用于改进Calderón-Zygmund算子与双线性Hilbert变换的界。

2021-04-11math.CAmath.FA

Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions

We study sharp frame bounds of Gabor frames with the standard Gaussian window and prove that the square lattice optimizes both the lower and the upper frame bound among all rectangular lattices. This proves a conjecture of Floch, Alard & Berrou (as reformulated by Strohmer & Beaver). The proof is based on refined log-convexity/concavity estimates for the Jacobi theta functions $θ_3$ and $θ_4$.

2016-09-06math.FA

Topological singular set of vector-valued maps, I: Applications to manifold-constrained Sobolev and BV spaces

We introduce an operator $\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a closed submanifold $N$ of the Euclidean space $\mathbb{R}^m$, and coincides with the distributional Jacobian in case $N$ is a sphere. The range of $\mathbf{S}$ is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. In this paper, we use $\mathbf{S}$ to characterise strong limits of smooth, $N$-valued maps with respect to Sobolev norm…

2018-12-17math.APmath.FA