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Blow-ups for the Horn–Kapranov parametrization of the classical discriminant 放大了经典判别式的Horn-Kapranov参数化
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-06-15 DOI: 10.4171/ecr/18-1/19
E. N. Mikhalkin, V. Stepanenko, A. K. Tsikh
{"title":"Blow-ups for the Horn–Kapranov parametrization of the classical discriminant","authors":"E. N. Mikhalkin, V. Stepanenko, A. K. Tsikh","doi":"10.4171/ecr/18-1/19","DOIUrl":"https://doi.org/10.4171/ecr/18-1/19","url":null,"abstract":"","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125772932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Counting bound states with maximal Fourier multipliers 用最大的傅里叶乘数计算束缚态
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-06-15 DOI: 10.4171/ecr/18-1/11
D. Hundertmark, P. Kunstmann, T. Ried, S. Vugalter
{"title":"Counting bound states with maximal Fourier multipliers","authors":"D. Hundertmark, P. Kunstmann, T. Ried, S. Vugalter","doi":"10.4171/ecr/18-1/11","DOIUrl":"https://doi.org/10.4171/ecr/18-1/11","url":null,"abstract":"","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121209020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ari Laptev and the Journal of Spectral Theory Ari Laptev和光谱理论杂志
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-06-15 DOI: 10.4171/ecr/18-1/3
E. B. Davies
{"title":"Ari Laptev and the Journal of Spectral Theory","authors":"E. B. Davies","doi":"10.4171/ecr/18-1/3","DOIUrl":"https://doi.org/10.4171/ecr/18-1/3","url":null,"abstract":"","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124370494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A version of Watson lemma for Laplace integrals and some applications 拉普拉斯积分的沃森引理的一个版本及其应用
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-06-15 DOI: 10.4171/ECR/18-1/17
S. Kupin, S. Naboko
{"title":"A version of Watson lemma for Laplace integrals and some applications","authors":"S. Kupin, S. Naboko","doi":"10.4171/ECR/18-1/17","DOIUrl":"https://doi.org/10.4171/ECR/18-1/17","url":null,"abstract":"","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128979753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wehrl-type coherent state entropy inequalities for SU(1,1) and its $AX+B$ subgroup SU(1,1)及其$AX+B$子群的wehrl型相干态熵不等式
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-06-15 DOI: 10.4171/ecr/18-1/18
E. Lieb, J. P. Solovej
{"title":"Wehrl-type coherent state entropy inequalities for SU(1,1) and its $AX+B$ subgroup","authors":"E. Lieb, J. P. Solovej","doi":"10.4171/ecr/18-1/18","DOIUrl":"https://doi.org/10.4171/ecr/18-1/18","url":null,"abstract":"Summary: We discuss the Wehrl-type entropy inequality conjecture for the group SU(1 , 1) and for its subgroup AX + B (or affine group), their representations on L 2 ( R + ) , and their coherent states. For AX + B the Wehrl-type conjecture for L p -norms of these coherent states (also known as the Renyi entropies) is proved in the case that p is an even integer. We also show how the general AX + B case reduces to an unsolved problem about analytic functions on the upper half-plane and the unit disk. For the entire collection see [Zbl 1465.35005].","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"63 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126273784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
The Feshbach–Schur map and perturbation theory Feshbach-Schur映射和微扰理论
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-05-05 DOI: 10.4171/ecr/18-1/5
Geneviève Dusson, I. Sigal, B. Stamm
{"title":"The Feshbach–Schur map and perturbation theory","authors":"Geneviève Dusson, I. Sigal, B. Stamm","doi":"10.4171/ecr/18-1/5","DOIUrl":"https://doi.org/10.4171/ecr/18-1/5","url":null,"abstract":"This paper deals with perturbation theory for discrete spectra of linear operators. To simplify exposition we consider here self-adjoint operators. This theory is based on the Feshbach-Schur map and it has advantages with respect to the standard perturbation theory in three aspects: (a) it readily produces rigorous estimates on eigenvalues and eigenfunctions with explicit constants; (b) it is compact and elementary (it uses properties of norms and the fundamental theorem of algebra about solutions of polynomial equations); and (c) it is based on a self-contained formulation of a fixed point problem for the eigenvalues and eigenfunctions, allowing for easy iterations. We apply our abstract results to obtain rigorous bounds on the ground states of Helium-type ions.","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129522805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Trace formulas for the modified Mathieu equation 修正后的Mathieu方程的迹公式
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-02-26 DOI: 10.4171/ecr/18-1/25
L. Takhtajan
{"title":"Trace formulas for the modified Mathieu equation","authors":"L. Takhtajan","doi":"10.4171/ecr/18-1/25","DOIUrl":"https://doi.org/10.4171/ecr/18-1/25","url":null,"abstract":"For the radial and one-dimensional Schr\"{o}dinger operator $H$ with growing potential $q(x)$ we outline a method of obtaining the trace identities - an asymptotic expansion of the Fredholm determinant $mathrm{det}_{F}(H-lambda I)$ as $lambdato-infty$. As an illustrating example, we consider Schr\"{o}dinger operator with the potential $q(x)=2cosh 2x$, associated with the modified Mathieu equation.","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125916746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A statistical theory of heavy atoms: Asymptotic behavior of the energy and stability of matter 重原子的统计理论:能量的渐近行为和物质的稳定性
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2021-01-16 DOI: 10.4171/ecr/18-1/23
H. Siedentop
{"title":"A statistical theory of heavy atoms: Asymptotic behavior of the energy and stability of matter","authors":"H. Siedentop","doi":"10.4171/ecr/18-1/23","DOIUrl":"https://doi.org/10.4171/ecr/18-1/23","url":null,"abstract":"We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation of the lower bound, we show stability of matter.","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132634459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Friedrichs-type inequalities in arbitrary domains 任意定义域中的friedrichs型不等式
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2020-11-30 DOI: 10.4171/ecr/18-1/2
A. Cianchi, V. Maz'ya
{"title":"Friedrichs-type inequalities in arbitrary domains","authors":"A. Cianchi, V. Maz'ya","doi":"10.4171/ecr/18-1/2","DOIUrl":"https://doi.org/10.4171/ecr/18-1/2","url":null,"abstract":"First and second-order inequalities of Friedrichs type for Sobolev functions in arbitrary domains are offered. The relevant inequalities involve optimal norms and constants that are independent of the geometry of the domain. Parallel inequalities for symmetric gradient Sobolev spaces of vector-valued functions are also presented. The results are derived via general criteria established in our earlier contributions [4] and [5].","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115487123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case 临界情况下奇异测度加权伪微分算子的特征值估计和渐近性
Partial Differential Equations, Spectral Theory, and Mathematical Physics Pub Date : 2020-11-30 DOI: 10.4171/ecr/18-1/20
G. Rozenblum, E. Shargorodsky
{"title":"Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case","authors":"G. Rozenblum, E. Shargorodsky","doi":"10.4171/ecr/18-1/20","DOIUrl":"https://doi.org/10.4171/ecr/18-1/20","url":null,"abstract":"In a domain $Omegasubset mathbb{R}^{mathbf{N}}$ we consider a selfadjoint operator $mathbf{T}=mathfrak{A}^*Pmathfrak{A} ,$ where $mathfrak{A}$ is a pseudodifferential operator of order $-l=-mathbf{N}/2$ and $P=Vmu_{Sigma}$ is a singular signed measure in $Omega$ concentrated on a Lipschitz surface $Sigma$ of dimension $d<mathbf{N}$, absolutely continuous with respect to the surface measure $mu_{Sigma}$ on $Sigma$. We establish eigenvalue estimates and asymptotics for this operator. It turns out that the order of these estimates and asymptotics is independent of the dimension $d$ of the surface. If there are several surfaces, possibly, of different dimensions, as well as an absolute continuous measure on $Omega$ the corresponding asymptotic coefficients add up.","PeriodicalId":125128,"journal":{"name":"Partial Differential Equations, Spectral Theory, and Mathematical Physics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131850089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
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