Journal of Spectral Theory最新文献_第3页

Johnson–Schwartzman gap labelling for ergodic Jacobi matrices 遍历Jacobi矩阵的Johnson-Schwartzman间隙标记

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-08-01 DOI: 10.4171/jst/449

D. Damanik, J. Fillman, Zhenghe Zhang

引用次数: 1

Limit theorems on the mesoscopic scale for the Anderson model Anderson模型介观尺度上的极限定理

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-04-28 DOI: 10.4171/jst/456

Yoel Grinshpon

引用次数: 0

Mikhail Shubin (1944–2020) 米哈伊尔·舒宾（1944–2020）

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-03-24 DOI: 10.4171/jst/391

M. Braverman, L. Friedlander

引用次数: 0

Spectral characteristics of Schrödinger operators generated by product systems 乘积系统产生的Schrödinger算子的谱特性

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-03-22 DOI: 10.4171/jst/445

D. Damanik, J. Fillman, P. Gohlke

{"title":"Spectral characteristics of Schrödinger operators generated by product systems","authors":"D. Damanik, J. Fillman, P. Gohlke","doi":"10.4171/jst/445","DOIUrl":"https://doi.org/10.4171/jst/445","url":null,"abstract":"We study ergodic Schr\"odinger operators defined over product dynamical systems in which one factor is periodic and the other factor is either a subshift over a finite alphabet or an irrational rotation of the circle. In the case in which one factor is a Boshernitzan subshift, we prove that either the resulting operators are periodic or the resulting spectra must be Cantor sets. The main ingredient is a suitable stability result for Boshernitzan's criterion under taking products. We also discuss the stability of purely singular continuous spectrum, which, given the zero-measure spectrum result, amounts to stability results for eigenvalue exclusion. In particular, we examine situations in which the existing criteria for the exclusion of eigenvalues are stable under periodic perturbations. As a highlight of this, we show that any simple Toeplitz subshift over a binary alphabet exhibits uniform absence of eigenvalues on the hull for any periodic perturbation whose period is commensurate with the coding sequence. In the case of a full shift, we give an effective criterion to compute exactly the spectrum of a random Anderson model perturbed by a potential of period two, and we further show that the naive generalization of this criterion does not hold for period three. Next, we consider quasi-periodic potentials with potentials generated by trigonometric polynomials with periodic background. We show that the quasiperiodic cocycle induced by passing to blocks of period length is subcritical when the coupling constant is small and supercritical when the coupling constant is large. Thus, the spectral type is absolutely continuous for small coupling and pure point (for a.e. frequency and phase) when the coupling is large.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49339054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Asymptotics of Robin eigenvalues on sharp infinite cones 锐无限锥上Robin特征值的渐近性

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-03-21 DOI: 10.4171/JST/452

Konstantin Pankrashkin, Marco Vogel

{"title":"Asymptotics of Robin eigenvalues on sharp infinite cones","authors":"Konstantin Pankrashkin, Marco Vogel","doi":"10.4171/JST/452","DOIUrl":"https://doi.org/10.4171/JST/452","url":null,"abstract":"Let $omegasubsetmathbb{R}^n$ be a bounded domain with Lipschitz boundary. For $varepsilon>0$ and $ninmathbb{N}$ consider the infinite cone $Omega_{varepsilon}:=big{(x_1,x')in (0,infty)timesmathbb{R}^n: x'invarepsilon x_1omegabig}subsetmathbb{R}^{n+1}$ and the operator $Q_{varepsilon}^{alpha}$ acting as the Laplacian $umapsto-Delta u$ on $Omega_{varepsilon}$ with the Robin boundary condition $partial_nu u=alpha u$ at $partialOmega_varepsilon$, where $partial_nu$ is the outward normal derivative and $alpha>0$. We look at the dependence of the eigenvalues of $Q_varepsilon^alpha$ on the parameter $varepsilon$: this problem was previously addressed for $n=1$ only (in that case, the only admissible $omega$ are finite intervals). In the present work we consider arbitrary dimensions $nge2$ and arbitrarily shaped\"cross-sections\"$omega$ and look at the spectral asymptotics as $varepsilon$ becomes small, i.e. as the cone becomes\"sharp\"and collapses to a half-line. It turns out that the main term of the asymptotics of individual eigenvalues is determined by the single geometric quantity $N_omega:=dfrac{mathrm{Vol}_{n-1} partialomega }{mathrm{Vol}_n omega}$. More precisely, for any fixed $jin mathbb{N}$ and $alpha>0$ the $j$th eigenvalue $E_j(Q^alpha_varepsilon)$ of $Q^alpha_varepsilon$ exists for all sufficiently small $varepsilon>0$ and satisfies $E_j(Q^alpha_varepsilon)=-dfrac{N_omega^2,alpha^2}{(2j+n-2)^2,varepsilon^2}+Oleft(dfrac{1}{varepsilon}right)$ as $varepsilonto 0^+$. The paper also covers some aspects of Sobolev spaces on infinite cones, which can be of independent interest.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46653152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Fractional Calderón problems and Poincaré inequalities on unbounded domains 无界域上的分数Calderón问题和Poincaré不等式

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-03-04 DOI: 10.4171/jst/444

J. Railo, Philipp Zimmermann

{"title":"Fractional Calderón problems and Poincaré inequalities on unbounded domains","authors":"J. Railo, Philipp Zimmermann","doi":"10.4171/jst/444","DOIUrl":"https://doi.org/10.4171/jst/444","url":null,"abstract":"We generalize many recent uniqueness results on the fractional Calder'on problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the characterization of uniqueness and nonuniqueness of partial data inverse problems for the fractional conductivity equation on domains that are bounded in one direction for conductivities supported in the whole Euclidean space and decaying to a constant background conductivity at infinity. We generalize the uniqueness proof for the fractional Calder'on problem by Ghosh, Salo and Uhlmann to a general abstract setting in order to use the full strength of their argument. This allows us to observe that there are also uniqueness results for many inverse problems for higher order local perturbations of a lower order fractional Laplacian. We give concrete example models to illustrate these curious situations and prove Poincar'e inequalities for the fractional Laplacians of any order on domains that are bounded in one direction. We establish Runge approximation results in these general settings, improve regularity assumptions also in the cases of bounded sets and prove general exterior determination results. Counterexamples to uniqueness in the inverse fractional conductivity problem with partial data are constructed in another companion work.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45629369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12

A growth estimate for the monodromy matrix of a canonical system 正则系统单矩阵的增长估计

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-02-28 DOI: 10.4171/jst/437

R. Pruckner, H. Woracek

引用次数: 1

Weyl laws for open quantum maps 开放量子映射的Weyl定律

IF 1 3区数学

Journal of Spectral Theory Pub Date : 2022-02-22 DOI: 10.4171/jst/441

Zhen-Hu Li

引用次数: 1

Boundary superconductivity in the BCS Model BCS模型中的边界超导性