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Functional Analysis and Its Applications最新文献

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The Quasilinear Parabolic Venttsel’ Problem with Discontinuous Leading Coefficients 前导系数不连续的准线性抛物线文特塞尔问题
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/s0016266323020065
D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova
{"title":"The Quasilinear Parabolic Venttsel’ Problem with Discontinuous Leading Coefficients","authors":"D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova","doi":"10.1134/s0016266323020065","DOIUrl":"https://doi.org/10.1134/s0016266323020065","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> New results on the strong solvability in Sobolev spaces of the quasilinear Venttsel’ problem for parabolic equations with discontinuous leading coefficients are obtained. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069352","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
Some Inequalities for $$p$$ -Quermassintegrals 关于 $$p$$ - 质点积分的一些不等式
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/s0016266323020028
Weidong Wang, Yanping Zhou
{"title":"Some Inequalities for $$p$$ -Quermassintegrals","authors":"Weidong Wang, Yanping Zhou","doi":"10.1134/s0016266323020028","DOIUrl":"https://doi.org/10.1134/s0016266323020028","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to <span>(p)</span>-quermassintegrals so that the cases <span>(p=1, -1, -n)</span> of <span>(p)</span>-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with <span>(p)</span>-quermassintegrals, including <span>(L_q)</span> Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069293","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 Birman Problem in the Theory of Nonnegative Symmetric Operators with Compact Inverse 论具有紧凑逆的非负对称算子理论中的比尔曼问题
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/s0016266323020090
M. M. Malamud
{"title":"On the Birman Problem in the Theory of Nonnegative Symmetric Operators with Compact Inverse","authors":"M. M. Malamud","doi":"10.1134/s0016266323020090","DOIUrl":"https://doi.org/10.1134/s0016266323020090","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Large classes of nonnegative Schrödinger operators on <span>(Bbb R^2)</span> and <span>(Bbb R^3)</span> with the following properties are described: </p><p> 1. The restriction of each of these operators to an appropriate unbounded set of measure zero in <span>(Bbb R^2)</span> (in <span>(Bbb R^3)</span>) is a nonnegative symmetric operator (the operator of a Dirichlet problem) with compact preresolvent; </p><p> 2. Under certain additional assumptions on the potential, the Friedrichs extension of such a restriction has continuous (sometimes absolutely continuous) spectrum filling the positive semiaxis. </p><p> The obtained results give a solution of a problem by M. S. Birman. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069478","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
Multipliers for the Calderón Construction 卡尔德龙建筑的乘数
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/s0016266323020016
E. I. Berezhnoi
{"title":"Multipliers for the Calderón Construction","authors":"E. I. Berezhnoi","doi":"10.1134/s0016266323020016","DOIUrl":"https://doi.org/10.1134/s0016266323020016","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> On the basis of a new approach to the Calderón construction <span>(X_0^{theta} X_1^{1-theta})</span> for ideal spaces <span>(X_0)</span> and <span>(X_1)</span> and a parameter <span>(theta in [0,1])</span>, final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces <span>(X_0)</span> and <span>(X_1)</span> have the Fatou property, then <span>(M(X_0^{theta_0} X_1^{1-theta_0},{to},X_0^{theta_1} X_1^{1-theta_1}) = M(X_1^{theta_1 - theta_0} to X_0^{theta_1 -theta_0}))</span> for <span>(0 &lt;theta_0 &lt;theta_1 &lt;1)</span>. Due to the absence of constraints on the ideal spaces <span>(X_0)</span> and <span>(X_1)</span>, the obtained results apply to a large class of ideal spaces. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069592","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
Diagram Automorphism Fixed Lie Algebras and Diagram Automorphism Fixed Quiver Varieties 图自形定列构和图自形定阙变式
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/s001626632302003x
Zhijie Dong, Haitao Ma
{"title":"Diagram Automorphism Fixed Lie Algebras and Diagram Automorphism Fixed Quiver Varieties","authors":"Zhijie Dong, Haitao Ma","doi":"10.1134/s001626632302003x","DOIUrl":"https://doi.org/10.1134/s001626632302003x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We define certain subvarieties, called <span>(theta)</span>-Hecke correspondences, in Cartesian products of diagram automorphism fixed quiver varieties. These give us generators of diagram automorphism fixed Lie algebras. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069471","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
Spectral Analysis of a Dynamical System Describing the Diffusion of Neutrons 描述中子扩散的动力系统的光谱分析
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/s0016266323020053
S. A. Stepin
{"title":"Spectral Analysis of a Dynamical System Describing the Diffusion of Neutrons","authors":"S. A. Stepin","doi":"10.1134/s0016266323020053","DOIUrl":"https://doi.org/10.1134/s0016266323020053","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The spectral properties of the generator of an evolution semigroup describing the dynamics of particle transport in a substance are studied. An effective estimate of the number of unstable modes is obtained, and geometric conditions for spectral stability and instability are found. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069401","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 Hyperbolic Equations: Operator Estimates with Correctors Taken into Account 双曲方程的均质化：考虑校正器的算子估算
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-01 DOI: 10.1134/s0016266323040093
{"title":"Homogenization of Hyperbolic Equations: Operator Estimates with Correctors Taken into Account","authors":"","doi":"10.1134/s0016266323040093","DOIUrl":"https://doi.org/10.1134/s0016266323040093","url":null,"abstract":"<span> <h3>Abstract</h3> <p> An elliptic second-order differential operator <span> <span>(A_varepsilon=b(mathbf{D})^*g(mathbf{x}/varepsilon)b(mathbf{D}))</span> </span> on <span> <span>(L_2(mathbb{R}^d))</span> </span> is considered, where <span> <span>(varepsilon &gt;0)</span> </span>, <span> <span>(g(mathbf{x}))</span> </span> is a positive definite and bounded matrix-valued function periodic with respect to some lattice, and <span> <span>(b(mathbf{D}))</span> </span> is a matrix first-order differential operator. Approximations for small <span> <span>(varepsilon)</span> </span> of the operator-functions <span> <span>(cos(tau A_varepsilon^{1/2}))</span> </span> and <span> <span>(A_varepsilon^{-1/2} sin (tau A_varepsilon^{1/2}))</span> </span> in various operator norms are obtained. The results can be applied to study the behavior of the solution of the Cauchy problem for the hyperbolic equation <span> <span>(partial^2_tau mathbf{u}_varepsilon(mathbf{x},tau) = - A_varepsilon mathbf{u}_varepsilon(mathbf{x},tau))</span> </span>. </p> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590251","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
The Cayley–Hamilton Theorem and Resolvent Representation 卡莱-汉密尔顿定理和残差表示法
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-01 DOI: 10.1134/s001626632304010x
{"title":"The Cayley–Hamilton Theorem and Resolvent Representation","authors":"","doi":"10.1134/s001626632304010x","DOIUrl":"https://doi.org/10.1134/s001626632304010x","url":null,"abstract":"<span> <h3>Abstract</h3> <p> For the Frobenius matrix accompanying an algebraic (differential) equation in a complex Banach algebra, the Cayley–Hamilton theorem is proved, which is used to obtain a representation of the resolvent. </p> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590225","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
Full Symmetric Toda System: Solution via QR-Decomposition 全对称户田系统：通过 QR 分解求解
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-01 DOI: 10.1134/s0016266323040081
{"title":"Full Symmetric Toda System: Solution via QR-Decomposition","authors":"","doi":"10.1134/s0016266323040081","DOIUrl":"https://doi.org/10.1134/s0016266323040081","url":null,"abstract":"<span> <h3>Abstract</h3> <p> The full symmetric Toda system is a generalization of the open Toda chain, for which the Lax operator is a symmetric matrix of general form. This system is Liouville integrable and even superintegrable. Deift, Lee, Nando, and Tomei (DLNT) proposed the chopping method for constructing integrals of such a system. In the paper, a solution of Hamiltonian equations for the entire family of DLNT integrals is constructed by using the generalized QR factorization method. For this purpose, certain tensor operations on the space of Lax operators and special differential operators on the Lie algebra are introduced. Both tools can be interpreted in terms of the representation theory of the Lie algebra <span> <span>(mathfrak{sl}_n)</span> </span> and are expected to generalize to arbitrary real semisimple Lie algebras. As is known, the full Toda system can be interpreted in terms of a compact Lie group and a flag space. Hopefully, the results on the trajectories of this system obtained in the paper will be useful in studying the geometry of flag spaces. </p> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590306","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
The Mumford Dynamical System and Hyperelliptic Kleinian Functions 芒福德动力系统和超椭圆克莱因函数
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-01 DOI: 10.1134/s0016266323040032
{"title":"The Mumford Dynamical System and Hyperelliptic Kleinian Functions","authors":"","doi":"10.1134/s0016266323040032","DOIUrl":"https://doi.org/10.1134/s0016266323040032","url":null,"abstract":"<span> <h3>Abstract</h3> <p> We develop a differential-algebraic theory of the Mumford dynamical system. In the framework of this theory, we introduce the <span> <span>((P,Q))</span> </span>-recursion, which defines a sequence of functions <span> <span>(P_1,P_2,ldots)</span> </span> given the first function <span> <span>(P_1)</span> </span> of this sequence and a sequence of parameters <span> <span>(h_1,h_2,dots)</span> </span>. The general solution of the <span> <span>((P,Q))</span> </span>-recursion is shown to give a solution for the parametric graded Korteweg–de Vries hierarchy. We prove that all solutions of the Mumford dynamical <span> <span>(g)</span> </span>-system are determined by the <span> <span>((P,Q))</span> </span>-recursion under the condition <span> <span>(P_{g+1} = 0)</span> </span>, which is equivalent to an ordinary nonlinear differential equation of order <span> <span>(2g)</span> </span> for the function <span> <span>(P_1)</span> </span>. Reduction of the <span> <span>(g)</span> </span>-system of Mumford to the Buchstaber–Enolskii–Leykin dynamical system is described explicitly, and its explicit <span> <span>(2g)</span> </span>-parameter solution in hyperelliptic Klein functions is presented. </p> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590222","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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