Functional Analysis and Its Applications最新文献_第3页

New Remarks on the Scattering for a Perturbed Polyharmonic Operator 关于摄动多谐算子散射的新注记

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030085

Grigori Rozenblum

引用次数: 0

A Generalized Birman–Schwinger Principle and Applications to One-Dimensional Schrödinger Operators with Distributional Potentials 广义Birman-Schwinger原理及其在一维Schrödinger分布势算子中的应用

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030024

Fritz Gesztesy, Roger Nichols

{"title":"A Generalized Birman–Schwinger Principle and Applications to One-Dimensional Schrödinger Operators with Distributional Potentials","authors":"Fritz Gesztesy, Roger Nichols","doi":"10.1134/S1234567825030024","DOIUrl":"10.1134/S1234567825030024","url":null,"abstract":" Given a self-adjoint operator (H_0) bounded from below in a complex, separable Hilbert space (mathcal H), the corresponding scale of spaces (mathcal H_{+1}(H_0) subset mathcal H subset mathcal H_{-1}(H_0)=[mathcal H_{+1}(H_0)]^*), and a fixed (Vin mathcal B(mathcal H_{+1}(H_0),mathcal H_{-1}(H_0))), we define the operator-valued map (A_V(,cdot,)colon rho(H_0)to mathcal B(mathcal H)) by where (rho(H_0)) denotes the resolvent set of (H_0). Assuming that (A_V(z)) is compact for some (z=z_0in rho(H_0)) and has norm strictly less than one for some (z=E_0in (-infty,0)), we employ an abstract version of Tiktopoulos’ formula to define an operator (H) in (mathcal H) that is formally realized as the sum of (H_0) and (V). We then establish a Birman–Schwinger principle for (H) in which (A_V(,cdot,)) plays the role of the Birman–Schwinger operator: (lambda_0in rho(H_0)) is an eigenvalue of (H) if and only if (1) is an eigenvalue of (A_V(lambda_0)). Furthermore, the geometric (but not necessarily the algebraic) multiplicities of (lambda_0) and (1) as eigenvalues of (H) and (A_V(lambda_0)), respectively, coincide. As a concrete application, we consider one-dimensional Schrödinger operators with (H^{-1}(mathbb{R})) distributional potentials. ","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"224 - 250"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Homogenization of the Lévy-type Operators lcv型算子的均匀化

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030036

Elena Zhizhina, Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina

{"title":"Homogenization of the Lévy-type Operators","authors":"Elena Zhizhina, Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina","doi":"10.1134/S1234567825030036","DOIUrl":"10.1134/S1234567825030036","url":null,"abstract":" In (L_2(mathbb R^d)), we consider a selfadjoint operator ({mathbb A}_varepsilon), (varepsilon >0), of the form where (0< alpha < 2). It is assumed that a function (mu(mathbf{x},mathbf{y})) is bounded, positive definite, periodic in each variable, and is such that (mu(mathbf{x},mathbf{y})=mu(mathbf{y},mathbf{x})). A rigorous definition of the operator ({mathbb A}_varepsilon) is given in terms of the corresponding quadratic form. It is proved that the resolvent (({mathbb A}_varepsilon+I)^{-1}) converges in the operator norm on (L_2(mathbb R^d)) to the operator (({mathbb A}^0+I)^{-1}) as (varepsilonto 0). Here, ({mathbb A}^0) is an effective operator of the same form with the constant coefficient (mu^0) equal to the mean value of (mu(mathbf{x},mathbf{y})). We obtain an error estimate of order (O(varepsilon^alpha)) for (0< alpha < 1), (O(varepsilon (1+| operatorname{ln} varepsilon|)^2)) for ( alpha=1), and (O(varepsilon^{2- alpha})) for (1< alpha < 2). In the case where (1< alpha < 2), the result is refined by taking the correctors into account. ","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"251 - 257"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Dmitri Rauelevich Yafaev (1948–2024) 德米特里·劳列维奇·亚法耶夫（1948-2024）

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030012

Editorial Board

引用次数: 0

Unbounded Integral Hankel Operators 无界积分汉克尔算子

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030073

Alexander Pushnitski, Sergei R. Treil

引用次数: 0

Eigenvalue Estimates for the Coulombic One-Particle Density Matrix and the Kinetic Energy Density Matrix 库仑单粒子密度矩阵和动能密度矩阵的特征值估计

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030103

Alexander Sobolev

{"title":"Eigenvalue Estimates for the Coulombic One-Particle Density Matrix and the Kinetic Energy Density Matrix","authors":"Alexander Sobolev","doi":"10.1134/S1234567825030103","DOIUrl":"10.1134/S1234567825030103","url":null,"abstract":" Consider a bound state (an eigenfunction) (psi) of an atom with (N) electrons. We study the spectra of the one-particle density matrix (gamma) and the one-particle kinetic energy density matrix (tau) associated with (psi). The paper contains two results. First, we obtain the bounds (lambda_k(gamma)le C k^{-8/3}) and (lambda_k(tau)le C k^{-2}) with some positive constants (C) that depend explicitly on the eigenfunction (psi). The sharpness of these bounds is confirmed by the asymptotic results obtained by the author in earlier papers. The advantage of these bounds over the ones derived by the author previously is their explicit dependence on the eigenfunction. Moreover, their new proofs are more elementary and direct. The second result is new, and it pertains to the case where the eigenfunction (psi) vanishes at the particle coalescence points. In particular, this is true for totally antisymmetric (psi). In this case, the eigenfunction (psi) exhibits enhanced regularity at the coalescence points, which leads to the faster decay of the eigenvalues: (lambda_k(gamma)le C k^{-10/3}) and (lambda_k(tau)le C k^{-8/3}). The proofs rely on estimates for the derivatives of the eigenfunction (psi) that depend explicitly on the distance to the coalescence points. Some of these estimates are borrowed directly from, and some are derived using the methods of, a recent paper by S. Fournais and T. Ø. Sørensen. ","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"347 - 365"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Eigenvalues of Non-Selfadjoint Functional Difference Operators 非自伴随泛函差分算子的特征值

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030048

Anna Zernova, Alexei Ilyin, Ari Laptev, Lukas Schimmer

引用次数: 0

Spectral Asymptotics for Robin Laplacians on Lipschitz Sets Lipschitz集上Robin laplace算子的谱渐近性

IF 0.7 4区数学

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030061

Simon Larson, Rupert L. Frank

引用次数: 0

The Speed of Convergence Under the Kolmogorov–Smirnov Metric in the Soshnikov Central Limit Theorem for the Sine Process Soshnikov中心极限定理下正弦过程在Kolmogorov-Smirnov度量下的收敛速度