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Surface Waves on Infinite Boundaries 无限边界上的表面波
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030115
Dmitrii Yafaev
{"title":"Surface Waves on Infinite Boundaries","authors":"Dmitrii Yafaev","doi":"10.1134/S1234567825030115","DOIUrl":"10.1134/S1234567825030115","url":null,"abstract":"<p> We develop scattering theory for the Laplace operator in the half-space with Robin type boundary conditions on the boundary plane. In particular, we show that, in addition to usual space waves living in cones and described by standard wave operators, surface waves may arise in this problem. They are localized in parabolic neighbourhoods of the boundary. We find conditions on the boundary coefficient ensuring the existence of surface waves. Several open problems are formulated. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"366 - 389"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1234567825030115.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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
{"title":"New Remarks on the Scattering for a Perturbed Polyharmonic Operator","authors":"Grigori Rozenblum","doi":"10.1134/S1234567825030085","DOIUrl":"10.1134/S1234567825030085","url":null,"abstract":"<p> We obtain sufficient conditions for the perturbation of the power of the resolvent of the polyharmonic operator under a perturbation by a highly singular potential to belong to Schatten classes. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"321 - 329"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316155","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
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,&nbsp;Roger Nichols","doi":"10.1134/S1234567825030024","DOIUrl":"10.1134/S1234567825030024","url":null,"abstract":"<p> Given a self-adjoint operator <span>(H_0)</span> bounded from below in a complex, separable Hilbert space <span>(mathcal H)</span>, the corresponding scale of spaces <span>(mathcal H_{+1}(H_0) subset mathcal H subset mathcal H_{-1}(H_0)=[mathcal H_{+1}(H_0)]^*)</span>, and a fixed <span>(Vin mathcal B(mathcal H_{+1}(H_0),mathcal H_{-1}(H_0)))</span>, we define the operator-valued map <span>(A_V(,cdot,)colon rho(H_0)to mathcal B(mathcal H))</span> by </p><p> where <span>(rho(H_0))</span> denotes the resolvent set of <span>(H_0)</span>. Assuming that <span>(A_V(z))</span> is compact for some <span>(z=z_0in rho(H_0))</span> and has norm strictly less than one for some <span>(z=E_0in (-infty,0))</span>, we employ an abstract version of Tiktopoulos’ formula to define an operator <span>(H)</span> in <span>(mathcal H)</span> that is formally realized as the sum of <span>(H_0)</span> and <span>(V)</span>. We then establish a Birman–Schwinger principle for <span>(H)</span> in which <span>(A_V(,cdot,))</span> plays the role of the Birman–Schwinger operator: <span>(lambda_0in rho(H_0))</span> is an eigenvalue of <span>(H)</span> if and only if <span>(1)</span> is an eigenvalue of <span>(A_V(lambda_0))</span>. Furthermore, the geometric (but not necessarily the algebraic) multiplicities of <span>(lambda_0)</span> and <span>(1)</span> as eigenvalues of <span>(H)</span> and <span>(A_V(lambda_0))</span>, respectively, coincide. </p><p> As a concrete application, we consider one-dimensional Schrödinger operators with <span>(H^{-1}(mathbb{R}))</span> distributional potentials. </p>","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,&nbsp;Andrey Piatnitski,&nbsp;Vladimir Sloushch,&nbsp;Tatiana Suslina","doi":"10.1134/S1234567825030036","DOIUrl":"10.1134/S1234567825030036","url":null,"abstract":"<p> In <span>(L_2(mathbb R^d))</span>, we consider a selfadjoint operator <span>({mathbb A}_varepsilon)</span>, <span>(varepsilon &gt;0)</span>, of the form </p><p> where <span>(0&lt; alpha &lt; 2)</span>. It is assumed that a function <span>(mu(mathbf{x},mathbf{y}))</span> is bounded, positive definite, periodic in each variable, and is such that <span>(mu(mathbf{x},mathbf{y})=mu(mathbf{y},mathbf{x}))</span>. A rigorous definition of the operator <span>({mathbb A}_varepsilon)</span> is given in terms of the corresponding quadratic form. It is proved that the resolvent <span>(({mathbb A}_varepsilon+I)^{-1})</span> converges in the operator norm on <span>(L_2(mathbb R^d))</span> to the operator <span>(({mathbb A}^0+I)^{-1})</span> as <span>(varepsilonto 0)</span>. Here, <span>({mathbb A}^0)</span> is an effective operator of the same form with the constant coefficient <span>(mu^0)</span> equal to the mean value of <span>(mu(mathbf{x},mathbf{y}))</span>. We obtain an error estimate of order <span>(O(varepsilon^alpha))</span> for <span>(0&lt; alpha &lt; 1)</span>, <span>(O(varepsilon (1+| operatorname{ln} varepsilon|)^2))</span> for <span>( alpha=1)</span>, and <span>(O(varepsilon^{2- alpha}))</span> for <span>(1&lt; alpha &lt; 2)</span>. In the case where <span>(1&lt; alpha &lt; 2)</span>, the result is refined by taking the correctors into account. </p>","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
Perron’s Method in the Dirichlet Problem for the Soft Laplacian on a Stratified Set 分层集上软拉普拉斯算子Dirichlet问题的Perron方法
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-17 DOI: 10.1134/S1064562424602658
N. S. Dairbekov, O. M. Penkin, D. V. Savasteev
{"title":"Perron’s Method in the Dirichlet Problem for the Soft Laplacian on a Stratified Set","authors":"N. S. Dairbekov,&nbsp;O. M. Penkin,&nbsp;D. V. Savasteev","doi":"10.1134/S1064562424602658","DOIUrl":"10.1134/S1064562424602658","url":null,"abstract":"<p>The solvability of the Dirichlet problem for the soft Laplacian on a stratified set is proved using a modification of the well-known Perron method.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"16 - 19"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316394","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
{"title":"Dmitri Rauelevich Yafaev (1948–2024)","authors":"Editorial Board","doi":"10.1134/S1234567825030012","DOIUrl":"10.1134/S1234567825030012","url":null,"abstract":"","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"221 - 223"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315639","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
On the Zaremba Problem for Inhomogeneous p-Laplace Equation with Drift 带漂移的非齐次p-Laplace方程的Zaremba问题
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-17 DOI: 10.1134/S1064562424602749
Yu. A. Alkhutov, M. D. Surnachev, A. G. Chechkina
{"title":"On the Zaremba Problem for Inhomogeneous p-Laplace Equation with Drift","authors":"Yu. A. Alkhutov,&nbsp;M. D. Surnachev,&nbsp;A. G. Chechkina","doi":"10.1134/S1064562424602749","DOIUrl":"10.1134/S1064562424602749","url":null,"abstract":"<p>A higher integrability of the gradient of a solution to the Zaremba problem in a bounded strictly Lipschitz domain is proved for an inhomogeneous <i>p</i>-Laplace equation with lower terms.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"1 - 5"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316134","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
On the Extraction of Random Bit Sequences in Quantum Random Number Generators with Several Independent Markov Sources 若干独立马尔可夫源量子随机数发生器中随机比特序列的提取
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-17 DOI: 10.1134/S1064562424602701
I. M. Arbekov, S. N. Molotkov
{"title":"On the Extraction of Random Bit Sequences in Quantum Random Number Generators with Several Independent Markov Sources","authors":"I. M. Arbekov,&nbsp;S. N. Molotkov","doi":"10.1134/S1064562424602701","DOIUrl":"10.1134/S1064562424602701","url":null,"abstract":"<p>The paper presents a method for extracting provably random bit sequences from several independent Markov chain trajectories, each having an arbitrary finite order. In implementing quantum random number generators, the combined use of several trajectories makes it possible to significantly increase the speed of generating output bit sequences.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"6 - 15"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316135","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
On Some Number Theoretic Sum 关于某些数论和
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-17 DOI: 10.1134/S1064562424601586
V. V. Iudelevich
{"title":"On Some Number Theoretic Sum","authors":"V. V. Iudelevich","doi":"10.1134/S1064562424601586","DOIUrl":"10.1134/S1064562424601586","url":null,"abstract":"<p>We obtain an asymptotic formula for the sum \u0000      <span>(Q(x) = sumlimits_{substack{ n leqslant x r(n + 1) ne 0 } } frac{{r(n)}}{{r(n + 1)}};;(x to + infty ),)</span> \u0000where <span>(r(n))</span> denotes the number of representations of <i>n</i> as a sum of two squares.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"25 - 28"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316396","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
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
{"title":"Unbounded Integral Hankel Operators","authors":"Alexander Pushnitski,&nbsp;Sergei R. Treil","doi":"10.1134/S1234567825030073","DOIUrl":"10.1134/S1234567825030073","url":null,"abstract":"<p> For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"297 - 320"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316154","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
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