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Functional Analysis and Its Applications最新文献

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A Semigroup of Paths on a Sequence of Uniformly Elliptic Complexes 均匀椭圆复数序列上的路径半群
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/S0016266323020041
I. A. Ivanov-Pogodaev
{"title":"A Semigroup of Paths on a Sequence of Uniformly Elliptic Complexes","authors":"I. A. Ivanov-Pogodaev","doi":"10.1134/S0016266323020041","DOIUrl":"10.1134/S0016266323020041","url":null,"abstract":"<p> The work is devoted to solving a problem of L. N. Shevrin and M. V. Sapir (Question 3.81b of the Sverdlovsk Notebook), namely, to constructing a finitely presented infinite nil-semigroup satisfying the identity <span>(x^9 = 0)</span>. This problem is solved with the help of geometric methods of the theory of tilings and aperiodic tessellations. A semigroup of paths on a tiling, under certain conditions, inherits some properties of the tiling itself. Moreover, the defining relations in the semigroup correspond to a set of equivalent paths on the tiling. </p><p> The relationship between the geometric and the automaton approaches previously used in the construction of finitely presented objects is discussed. As noted by S. P. Novikov, the property of determinacy in the coloring of partition nodes and its extension inward is very similar to properties of a solution of a partial differential equation with a given boundary condition. The author believes that understanding this relationship between the theories of aperiodic mosaics and their arrangements and the theory of numerical methods and grids is very promising. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"117 - 142"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069407","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 0.6 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,&nbsp;Yanping Zhou","doi":"10.1134/S0016266323020028","DOIUrl":"10.1134/S0016266323020028","url":null,"abstract":"<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":"57 2","pages":"99 - 108"},"PeriodicalIF":0.6,"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 0.6 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":"10.1134/S0016266323020090","url":null,"abstract":"<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":"57 2","pages":"173 - 177"},"PeriodicalIF":0.6,"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 0.6 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":"10.1134/S0016266323020016","url":null,"abstract":"<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":"57 2","pages":"87 - 98"},"PeriodicalIF":0.6,"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 0.6 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,&nbsp;Haitao Ma","doi":"10.1134/S001626632302003X","DOIUrl":"10.1134/S001626632302003X","url":null,"abstract":"<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":"57 2","pages":"109 - 116"},"PeriodicalIF":0.6,"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 0.6 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":"10.1134/S0016266323020053","url":null,"abstract":"<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":"57 2","pages":"143 - 157"},"PeriodicalIF":0.6,"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
Connes Integration Formula: A Constructive Approach cones积分公式:一个建设性的方法
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-09-05 DOI: 10.1134/S0016266323010045
D. V. Zanin, F. A. Sukochev
{"title":"Connes Integration Formula: A Constructive Approach","authors":"D. V. Zanin,&nbsp;F. A. Sukochev","doi":"10.1134/S0016266323010045","DOIUrl":"10.1134/S0016266323010045","url":null,"abstract":"<p> A version of Connes Integration Formula which provides concrete asymptotics of eigenvalues is given. This radically extends the class of quantum-integrable functions on compact Riemannian manifolds. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"40 - 59"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4231634","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 Image of a Lagrangian Germ of Type (E_6^pm) 拉格朗日型胚芽的象 (E_6^pm)
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-09-05 DOI: 10.1134/S0016266323010094
V. D. Sedykh
{"title":"The Image of a Lagrangian Germ of Type (E_6^pm)","authors":"V. D. Sedykh","doi":"10.1134/S0016266323010094","DOIUrl":"10.1134/S0016266323010094","url":null,"abstract":"<p> It is proved that the image of a stable germ of type <span>(E_6^pm)</span> of a Lagrangian map to <span>(mathbb R^n)</span> is homeomorphic to the germ at zero of a closed half-space. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"80 - 82"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233945","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 Structure of Coset (n)-Valued Topological Groups on (S^3) and (mathbb{R}P^3) 关于(S^3)和上的陪集(n)值拓扑群的结构 (mathbb{R}P^3)
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-09-05 DOI: 10.1134/S0016266323010070
D. V. Gugnin
{"title":"On the Structure of Coset (n)-Valued Topological Groups on (S^3) and (mathbb{R}P^3)","authors":"D. V. Gugnin","doi":"10.1134/S0016266323010070","DOIUrl":"10.1134/S0016266323010070","url":null,"abstract":"<p> Three-dimensional manifolds carrying the structure of <span>(n)</span>-valued coset topological groups originating from the Lie groups <span>(Sp(1))</span> and <span>(SO(3))</span> are classified. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"71 - 73"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233948","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
Nash-Type Inequalities on Metric-Measure Spaces 度量-测度空间上的纳什型不等式
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-09-05 DOI: 10.1134/S0016266323010069
A. Ranjbar-Motlagh
{"title":"Nash-Type Inequalities on Metric-Measure Spaces","authors":"A. Ranjbar-Motlagh","doi":"10.1134/S0016266323010069","DOIUrl":"10.1134/S0016266323010069","url":null,"abstract":"<p> We extend homogeneous and inhomogeneous Nash-type inequalities to abstract metric-measure spaces. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"65 - 70"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235132","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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