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Functional Analysis and Its Applications最新文献

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On a Sharp Lower Bound for the Tjurina Number of Zero-Dimensional Complete Intersections 零维完全交点Tjurina数的一个尖锐下界
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-09-05 DOI: 10.1134/S001626632301001X
A. G. Aleksandrov
{"title":"On a Sharp Lower Bound for the Tjurina Number of Zero-Dimensional Complete Intersections","authors":"A. G. Aleksandrov","doi":"10.1134/S001626632301001X","DOIUrl":"10.1134/S001626632301001X","url":null,"abstract":"<p> As is known, for isolated hypersurface singularities and complete intersections of positive dimension, the Milnor number is the least upper bound for the Tjurina number, i.e., <span>(tau leqslant mu)</span>. In this paper we show that, for zero-dimensional complete intersections, the reverse inequality holds. The proof is based on properties of faithful modules over an Artinian local ring. We also exploit simple properties of the annihilator and the socle of the modules of Kähler differentials and derivations and the theory of duality in the cotangent complex of zero-dimensional singularities. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4231633","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
Self-Joinings and Generic Extensions of Ergodic Systems Ergodic 系统的自连接和通用扩展
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-09-01 DOI: 10.1134/s0016266323030048
{"title":"Self-Joinings and Generic Extensions of Ergodic Systems","authors":"","doi":"10.1134/s0016266323030048","DOIUrl":"https://doi.org/10.1134/s0016266323030048","url":null,"abstract":"<span> <h3>Abstract</h3> <p> It is proved that the generic extensions of a dynamical system inherit the triviality of pairwise independent self-joinings. This property is related to well-known problems of joining theory and to Rokhlin’s famous multiple mixing problem. </p> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128282","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 Convergence Rate Estimate for Remotest Projections on Three Subspaces 三个子空间上最远投影的收敛率估算
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-06-01 DOI: 10.1134/s0016266323020077
{"title":"A Convergence Rate Estimate for Remotest Projections on Three Subspaces","authors":"","doi":"10.1134/s0016266323020077","DOIUrl":"https://doi.org/10.1134/s0016266323020077","url":null,"abstract":"<span> <h3>Abstract</h3> <p> We give an estimate of the rate of convergence to zero of the norms of remotest projections on three subspaces of a Hilbert space with zero intersection for starting vectors in the sum of orthogonal complements to these subspaces. </p> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069408","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 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 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-06-01 DOI: 10.1134/s0016266323020041
{"title":"A Semigroup of Paths on a Sequence of Uniformly Elliptic Complexes","authors":"","doi":"10.1134/s0016266323020041","DOIUrl":"https://doi.org/10.1134/s0016266323020041","url":null,"abstract":"<span> <h3>Abstract</h3> <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> <span>(x^9 = 0)</span> </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> </span>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-06-01","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
On Bloch Solutions of Difference Schrödinger Equations 差分Schrödinger方程的Bloch解
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040013
D. I. Borisov, A. A. Fedotov
{"title":"On Bloch Solutions of Difference Schrödinger Equations","authors":"D. I. Borisov,&nbsp;A. A. Fedotov","doi":"10.1134/S0016266322040013","DOIUrl":"10.1134/S0016266322040013","url":null,"abstract":"<p> Bloch solutions of the difference Schrödinger equation with periodic complex potential on the real line are discussed. The case where the spectral parameter is outside the spectrum of the corresponding Schrödinger operator is considered. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4525197","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: 1
Hermitian Property and the Simplicity of Spectrum of Bethe Subalgebras in Yangians yangian中Bethe子代数的厄米性质和谱的简单性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040098
I. A. Mashanova-Golikova
{"title":"Hermitian Property and the Simplicity of Spectrum of Bethe Subalgebras in Yangians","authors":"I. A. Mashanova-Golikova","doi":"10.1134/S0016266322040098","DOIUrl":"10.1134/S0016266322040098","url":null,"abstract":"<p> The image of the Bethe subalgebra <span>(B(C))</span> in the tensor product of representations of the Yangian <span>(Y(mathfrak{gl}_n))</span> contains the full set of Hamiltonians of the Heisenberg magnet chain XXX. The main problem in the XXX integrable system is the diagonalization of the operators by which the elements of Bethe subalgebras act on the corresponding representations of the Yangian. The standard approach is the Bethe ansatz. As the first step toward solving this problem, we want to show that the eigenvalues of these operators have multiplicity 1. In this work we obtained several new results on the simplicity of spectra of Bethe subalgebras in Kirillov–Reshetikhin modules in the case of <span>(Y(mathfrak{g}))</span>, where <span>(mathfrak{g})</span> is a simple Lie algebra. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4519465","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
One-Dimensional Central Measures on Numberings of Ordered Sets 有序集编号的一维中心测度
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040025
A. M. Vershik
{"title":"One-Dimensional Central Measures on Numberings of Ordered Sets","authors":"A. M. Vershik","doi":"10.1134/S0016266322040025","DOIUrl":"10.1134/S0016266322040025","url":null,"abstract":"<p> We describe one-dimensional central measures on numberings (tableaux) of ideals of partially ordered sets (posets). As the main example, we study the poset <span>(mathbb{Z}_+^d)</span> and the graph of its finite ideals, multidimensional Young tableaux; for <span>(d=2)</span>, this is the ordinary Young graph. The central measures are stratified by dimension; in the paper we give a complete description of the one-dimensional stratum and prove that every ergodic central measure is uniquely determined by its frequencies. The suggested method, in particular, gives the first purely combinatorial proof of E. Thoma’s theorem for one-dimensional central measures different from the Plancherel measure (which is of dimension <span>(2)</span>). </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4521274","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 Extension of Functions from Countable Subspaces 论可数子空间中函数的可拓性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040049
A. Yu. Groznova
{"title":"On the Extension of Functions from Countable Subspaces","authors":"A. Yu. Groznova","doi":"10.1134/S0016266322040049","DOIUrl":"10.1134/S0016266322040049","url":null,"abstract":"<p> Three intermediate class of spaces <span>(mathscr{R}_1subset mathscr{R}_2subset mathscr{R}_3)</span> between the classes of <span>(F)</span>- and <span>(betaomega)</span>-spaces are considered. The <span>(mathscr{R}_1)</span>- and <span>(mathscr{R}_3)</span>-spaces are characterized in terms of the extension of functions. It is proved that the classes of <span>(mathscr{R}_1)</span>-, <span>(mathscr{R}_2)</span>-, <span>(mathscr{R}_3)</span>-, and <span>(betaomega)</span>-spaces are not preserved by the Stone–Čech compactification. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4524184","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
Superposition Principle for the Fokker–Planck–Kolmogorov Equations with Unbounded Coefficients 系数无界的Fokker-Planck-Kolmogorov方程的叠加原理
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040062
T. I. Krasovitskii, S. V. Shaposhnikov
{"title":"Superposition Principle for the Fokker–Planck–Kolmogorov Equations with Unbounded Coefficients","authors":"T. I. Krasovitskii,&nbsp;S. V. Shaposhnikov","doi":"10.1134/S0016266322040062","DOIUrl":"10.1134/S0016266322040062","url":null,"abstract":"<p> The superposition principle delivers a probabilistic representation of a solution <span>({mu_t}_{tin[0, T]})</span> of the Fokker–Planck–Kolmogorov equation <span>(partial_tmu_t=L^{*}mu_t)</span> in terms of a solution <span>(P)</span> of the martingale problem with operator <span>(L)</span>. We generalize the superposition principle to the case of equations on a domain, examine the transformation of the measure <span>(P)</span> and the operator <span>(L)</span> under a change of variables, and obtain new conditions for the validity of the superposition principle under the assumption of the existence of a Lyapunov function for the unbounded part of the drift coefficient. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4519435","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
Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients 二阶周期系数算子齐次化的改进求解逼近
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040086
S. E. Pastukhova
{"title":"Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients","authors":"S. E. Pastukhova","doi":"10.1134/S0016266322040086","DOIUrl":"10.1134/S0016266322040086","url":null,"abstract":"<p> For elliptic divergent self-adjoint second-order operators with <span>(varepsilon)</span>-periodic measurable coefficients acting on the whole space <span>(mathbb{R}^d)</span>, resolvent approximations in the operator norm <span>(|!,boldsymbolcdot,!|_{H^1to H^1})</span> with remainder of order <span>(varepsilon^2)</span> as <span>(varepsilonto 0)</span> are found by the method of two-scale expansions with the use of smoothing. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4525641","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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