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Eigenfunctions growth of R-limits on graphs 图上R-极限的特征函数增长
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-12-02 DOI: 10.4171/jst/389
Siegfried Beckus, Latif Eliaz
{"title":"Eigenfunctions growth of R-limits on graphs","authors":"Siegfried Beckus, Latif Eliaz","doi":"10.4171/jst/389","DOIUrl":"https://doi.org/10.4171/jst/389","url":null,"abstract":"","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41711288","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: 0
Spectrum of the semi-relativistic Pauli–Fierz model II 半相对论Pauli-Fierz模型的谱2
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-12-02 DOI: 10.4171/jst/386
Takeru Hidaka, Fumio Hiroshima, Itaru Sasaki
{"title":"Spectrum of the semi-relativistic Pauli–Fierz model II","authors":"Takeru Hidaka, Fumio Hiroshima, Itaru Sasaki","doi":"10.4171/jst/386","DOIUrl":"https://doi.org/10.4171/jst/386","url":null,"abstract":"We consider the ground state of the semi-relativistic Pauli–Fierz Hamiltonian $$ H = |textbf{p} - textbf{A(x)}| + H_f + Vtextbf{(x)}. $$ Here $textbf{A(x)}$ denotes the quantized radiation field with an ultraviolet cutoff function and $H_f$ the free field Hamiltonian with dispersion relation $|textbf{k}|$. The Hamiltonian $H$ describes the dynamics of a <i>massless</i> and semi-relativistic charged particle interacting with the quantized radiation field with an ultraviolet cutoff function. In 2016, the first two authors proved the existence of the ground state $Phi_m$ of the massive Hamiltonian $H_m$ is proven. Here, the massive Hamiltonian $H_m$ is defined by $H$ with dispersion relation $sqrt{textbf{k}^2+m^2}$ $(m&gt;0)$. In this paper, the existence of the ground state of $H$ is proven. To this aim, we estimate a singular and non-local pull-through formula and show the equicontinuity of ${a(k)Phi_m}_{0<m<m_0}$ ${phi_m}_{0<m<m_0}$,=\"\" $a(k)$=\"\" $h$=\"\" $m_0$,=\"\" annihilation=\"\" compactness=\"\" denotes=\"\" existence=\"\" formal=\"\" ground=\"\" is=\"\" kernel=\"\" of=\"\" operator.=\"\" set=\"\" showing=\"\" shown.<=\"\" some=\"\" span=\"\" state=\"\" the=\"\" where=\"\" with=\"\">\u0000</m<m_0}$>","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532060","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: 0
The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds 三维共形Stäckel流形的各向异性Calderón问题
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-12-02 DOI: 10.4171/jst/384
Thierry Daudé, N. Kamran, F. Nicoleau
{"title":"The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds","authors":"Thierry Daudé, N. Kamran, F. Nicoleau","doi":"10.4171/jst/384","DOIUrl":"https://doi.org/10.4171/jst/384","url":null,"abstract":"","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41819919","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: 1
Erratum to “Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains” “凸域上Dirichlet拉普拉斯算子Riesz均值的渐近形状优化”的勘误表
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-11-02 DOI: 10.4171/jst/383
S. Larson
{"title":"Erratum to “Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains”","authors":"S. Larson","doi":"10.4171/jst/383","DOIUrl":"https://doi.org/10.4171/jst/383","url":null,"abstract":"","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47574052","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: 1
A theorem on the multiplicity of the singular spectrum of a general Anderson-type Hamiltonian 一般安德森型哈密顿算子奇异谱的多重性定理
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-11-02 DOI: 10.4171/jst/374
D. R. Dolai, Anish Mallick
{"title":"A theorem on the multiplicity of the singular spectrum of a general Anderson-type Hamiltonian","authors":"D. R. Dolai, Anish Mallick","doi":"10.4171/jst/374","DOIUrl":"https://doi.org/10.4171/jst/374","url":null,"abstract":"Summary: In this work, we study the multiplicity of the singular spectrum for operators of the form A ω = A + ∑ n ω n C n on a separable Hilbert space H , where A is a self-adjoint operator and { C n } n is a countable collection of non-negative finite-rank operators. When { ω n } n are independent real random variables with absolutely continuous distributions, we show that the multiplicity of the singular spectrum is almost surely bounded above by the maximum algebraic multiplicity of the eigenvalues of the operator √ C n ( A ω − z ) − 1 √ C n for all n and almost all ( z, ω ) . The result is optimal in the sense that there are operators for which the bound is achieved. We also provide an effective bound on the multiplicity of the singular spectrum for some special cases.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43871355","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: 0
Anderson localization for a generalized Maryland model with potentials given by skew shifts 具有斜移势的广义Maryland模型的Anderson局部化
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-09-20 DOI: 10.4171/jst/373
Jia Shi, Xiaoping Yuan
{"title":"Anderson localization for a generalized Maryland model with potentials given by skew shifts","authors":"Jia Shi, Xiaoping Yuan","doi":"10.4171/jst/373","DOIUrl":"https://doi.org/10.4171/jst/373","url":null,"abstract":"","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45961053","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: 0
The fate of Landau levels under $delta$-interactions $delta$相互作用下朗道能级的命运
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-09-15 DOI: 10.4171/jst/422
J. Behrndt, M. Holzmann, V. Lotoreichik, G. Raikov
{"title":"The fate of Landau levels under $delta$-interactions","authors":"J. Behrndt, M. Holzmann, V. Lotoreichik, G. Raikov","doi":"10.4171/jst/422","DOIUrl":"https://doi.org/10.4171/jst/422","url":null,"abstract":"We consider the self-adjoint Landau Hamiltonian $H_0$ in $L^2(mathbb{R}^2)$ whose spectrum consists of infinitely degenerate eigenvalues $Lambda_q$, $q in mathbb{Z}_+$, and the perturbed operator $H_upsilon = H_0 + upsilondelta_Gamma$, where $Gamma subset mathbb{R}^2$ is a regular Jordan $C^{1,1}$-curve, and $upsilon in L^p(Gamma;mathbb{R})$, $p>1$, has a constant sign. We investigate ${rm Ker}(H_upsilon -Lambda_q)$, $q in mathbb{Z}_+$, and show that generically $$0 leq {rm dim , Ker}(H_upsilon -Lambda_q) - {rm dim , Ker}(T_q(upsilon delta_Gamma))<infty,$$ where $T_q(upsilon delta_Gamma) = p_q (upsilon delta_Gamma)p_q$, is an operator of Berezin-Toeplitz type, acting in $p_q L^2(mathbb{R}^2)$, and $p_q$ is the orthogonal projection on ${rm Ker},(H_0 -Lambda_q)$. If $upsilon neq 0$ and $q = 0$, we prove that ${rm Ker},(T_0(upsilon delta_Gamma)) = {0}$. If $q geq 1$, and $Gamma = mathcal{C}_r$ is a circle of radius $r$, we show that ${rm dim , Ker} (T_q(delta_{mathcal{C}_r})) leq q$, and the set of $r in (0,infty)$ for which ${rm dim , Ker}(T_q(delta_{mathcal{C}_r})) geq 1$, is infinite and discrete.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44674885","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: 0
On inverse problems arising in fractional elasticity 分数阶弹性的反问题
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-09-08 DOI: 10.4171/jst/428
Li Li
{"title":"On inverse problems arising in fractional elasticity","authors":"Li Li","doi":"10.4171/jst/428","DOIUrl":"https://doi.org/10.4171/jst/428","url":null,"abstract":"We first formulate an inverse problem for a linear fractional Lam'e system. We determine the Lam'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an inverse problem for a nonlinear fractional Lam'e system. Our arguments are based on the unique continuation property for the fractional operator as well as the associated Runge approximation property.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42972862","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: 9
Different completions of $A + CX$ $A + CX$的不同完成方式
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-07-30 DOI: 10.4171/jst/356
D. Cvetković-Ilić, Qingwen Wang, Yimin Wei
{"title":"Different completions of $A + CX$","authors":"D. Cvetković-Ilić, Qingwen Wang, Yimin Wei","doi":"10.4171/jst/356","DOIUrl":"https://doi.org/10.4171/jst/356","url":null,"abstract":"","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48605590","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: 0
Fine dimensional properties of spectral measures 光谱测量的精细维度特性
IF 1 3区 数学
Journal of Spectral Theory Pub Date : 2021-07-22 DOI: 10.4171/jst/436
M. Landrigan, M. Powell
{"title":"Fine dimensional properties of spectral measures","authors":"M. Landrigan, M. Powell","doi":"10.4171/jst/436","DOIUrl":"https://doi.org/10.4171/jst/436","url":null,"abstract":"Operators with zero dimensional spectral measures appear naturally in the theory of ergodic Schr\"odinger operators. We develop the concept of a complete family of Hausdorff measure functions in order to analyze and distinguish between these measures with any desired precision. We prove that the dimension of spectral measures of half-line operators with positive upper Lyapunov exponent are at most logarithmic for every possible boundary phase. We show that this is sharp by constructing an explicit operator whose spectral measure obtains this dimension. We also extend and improve some basic results from the theory of rank one perturbations and quantum dynamics to encompass generalized Hausdorff dimensions.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47026487","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: 3
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