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Functional Analysis and Its Applications最新文献

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Resolution of Singularities of the Odd Nilpotent Cone of Orthosymplectic Lie Superalgebras 正交列超拉的奇数无势锥的奇点解析
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S0016266323030024
I. D. Motorin
{"title":"Resolution of Singularities of the Odd Nilpotent Cone of Orthosymplectic Lie Superalgebras","authors":"I. D. Motorin","doi":"10.1134/S0016266323030024","DOIUrl":"10.1134/S0016266323030024","url":null,"abstract":"<p> We construct a Springer-type resolution of singularities of the odd nilpotent cone of the orthosymplectic Lie superalgebras <span>(mathfrak{osp}(m|2n))</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"192 - 207"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128334","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
Two-Dimensional Diffusion Orthogonal Polynomials Ordered by a Weighted Degree 按加权度排序的二维扩散正交多项式
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S0016266323030036
S. Yu. Orevkov
{"title":"Two-Dimensional Diffusion Orthogonal Polynomials Ordered by a Weighted Degree","authors":"S. Yu. Orevkov","doi":"10.1134/S0016266323030036","DOIUrl":"10.1134/S0016266323030036","url":null,"abstract":"<p> We study the problem of describing the triples <span>((Omega,g,mu))</span>, <span>(mu=rho,dx)</span>, where <span>(g= (g^{ij}(x)))</span> is the (co)metric associated with a symmetric second-order differential operator <span>(mathbf{L}(f) = frac{1}{rho}sum_{ij} partial_i (g^{ij} rho,partial_j f))</span> defined on a domain <span>(Omega)</span> of <span>(mathbb{R}^d)</span> and such that there exists an orthonormal basis of <span>(mathcal{L}^2(mu))</span> consisting of polynomials which are eigenvectors of <span>(mathbf{L})</span> and this basis is compatible with the filtration of the space of polynomials by some weighted degree. </p><p> In a joint paper of D. Bakry, M. Zani, and the author this problem was solved in dimension 2 for the usual degree. In the present paper we solve it still in dimension 2 but for a weighted degree with arbitrary positive weights. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"208 - 235"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128265","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
Resurgence and Partial Theta Series 复活和部分 Theta 系列
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S001626632303005X
Li Han, Yong Li, David Sauzin, Shanzhong Sun
{"title":"Resurgence and Partial Theta Series","authors":"Li Han,&nbsp;Yong Li,&nbsp;David Sauzin,&nbsp;Shanzhong Sun","doi":"10.1134/S001626632303005X","DOIUrl":"10.1134/S001626632303005X","url":null,"abstract":"<p> We consider partial theta series associated with periodic sequences of coefficients, namely, <span>(Theta(tau):= sum_{n&gt;0} n^nu f(n) e^{ipi n^2tau/M})</span>, where <span>(nuinmathbb{Z}_{ge0})</span> and </p><p> <span>(fcolonmathbb{Z} to mathbb{C})</span> is an <span>(M)</span>-periodic function. Such a function <span>(Theta)</span> is analytic in the half-plane <span>({ operatorname {Im}tau&gt;0})</span> and in the asymptotics of <span>(Theta(tau))</span> as <span>(tau)</span> tends nontangentially to any <span>(alphainmathbb{Q})</span> a formal power series appears, which depends on the parity of <span>(nu)</span> and <span>(f)</span>. We discuss the summability and resurgence properties of these series; namely, we present explicit formulas for their formal Borel transforms and their consequences for the modularity properties of <span>(Theta)</span>, or its “quantum modularity” properties in the sense of Zagier’s recent theory. The discrete Fourier transform of <span>(f)</span> plays an unexpected role and leads to a number-theoretic analogue of Écalle’s “bridge equations.” The main thesis is: (quantum) modularity <span>(=)</span> Stokes phenomenon <span>(+)</span> discrete Fourier transform. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"248 - 265"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128269","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 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/S0016266323020077
P. A. Borodin, L. Sh. Burusheva
{"title":"A Convergence Rate Estimate for Remotest Projections on Three Subspaces","authors":"P. A. Borodin,&nbsp;L. Sh. Burusheva","doi":"10.1134/S0016266323020077","DOIUrl":"10.1134/S0016266323020077","url":null,"abstract":"<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>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"164 - 168"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","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
Limit Spectral Measures of Matrix Distributions of Metric Triples 度量三元矩阵分布的极限谱量
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/S0016266323020089
A. M. Vershik, F. V. Petrov
{"title":"Limit Spectral Measures of Matrix Distributions of Metric Triples","authors":"A. M. Vershik,&nbsp;F. V. Petrov","doi":"10.1134/S0016266323020089","DOIUrl":"10.1134/S0016266323020089","url":null,"abstract":"<p> The notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coincides with the spectrum of the integral operator on <span>(L^2(mu))</span> with kernel <span>(rho)</span>. An example in which there is no deterministic spectral measure is constructed. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"169 - 172"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069351","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 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 0.6 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,&nbsp;A. I. Nazarov,&nbsp;D. K. Palagachev,&nbsp;L. G. Softova","doi":"10.1134/S0016266323020065","DOIUrl":"10.1134/S0016266323020065","url":null,"abstract":"<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":"57 2","pages":"158 - 163"},"PeriodicalIF":0.6,"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
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
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