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Bundles of Holomorphic Function Algebras on Subvarieties of the Noncommutative Ball 非交换球子变量上的全态函数代数束
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030043
Maria Dmitrieva
{"title":"Bundles of Holomorphic Function Algebras on Subvarieties of the Noncommutative Ball","authors":"Maria Dmitrieva","doi":"10.1134/S0016266324030043","DOIUrl":"10.1134/S0016266324030043","url":null,"abstract":"<p> We suggest a general construction of continuous Banach bundles of holomorphic function algebras on subvarieties of the closed noncommutative ball. These algebras are of the form <span>(mathcal{A}_d/overline{I_x})</span>, where <span>(mathcal{A}_d)</span> is the noncommutative disc algebra defined by G. Popescu, and <span>(overline{I_x})</span> is the closure in <span>(mathcal{A}_d)</span> of a graded ideal <span>(I_x)</span> in the algebra of noncommutative polynomials, depending continuously on a point <span>(x)</span> of a topological space <span>(X)</span>. Moreover, we construct bundles of Fréchet algebras <span>(mathcal{F}_d/overline{I_x})</span> of holomorphic functions on subvarieties of the open noncommutative ball. The algebra <span>(mathcal{F}_d)</span> of free holomorphic functions on the unit ball was also introduced by G. Popescu, and <span>(overline{I_x})</span> stands for the closure in <span>(mathcal{F}_d)</span> of a graded ideal <span>(I_x)</span> in the algebra of noncommutative polynomials, depending continuously on a point <span>(xin X)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"268 - 288"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434940","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
Publisher Correction to: Noncommutative Geometry of Random Surfaces, Funct. Anal. Appl. 58:1 (2024), 65–79 Publisher Correction to：Noncommutative Geometry of Random Surfaces, Funct. Anal.Anal.58:1 (2024), 65-79
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030110
Andrei Okounkov
{"title":"Publisher Correction to: Noncommutative Geometry of Random Surfaces, Funct. Anal. Appl. 58:1 (2024), 65–79","authors":"Andrei Okounkov","doi":"10.1134/S0016266324030110","DOIUrl":"10.1134/S0016266324030110","url":null,"abstract":"","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"347 - 347"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0016266324030110.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434885","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
Elliptic Cauchy Matrices 椭圆考奇矩阵
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030055
Anton Zabrodin, Vadim Prokofev
{"title":"Elliptic Cauchy Matrices","authors":"Anton Zabrodin,&nbsp;Vadim Prokofev","doi":"10.1134/S0016266324030055","DOIUrl":"10.1134/S0016266324030055","url":null,"abstract":"<p> Some identities that involve the elliptic version of the Cauchy matrices are presented and proved. They include the determinant formula, the formula for the inverse matrix, the matrix product identity and the factorization formula. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"289 - 298"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434938","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 Distribution of Eigenvalues of Nuclear Operators 论核算子特征值的分布
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030109
Oleg Reinov
{"title":"On the Distribution of Eigenvalues of Nuclear Operators","authors":"Oleg Reinov","doi":"10.1134/S0016266324030109","DOIUrl":"10.1134/S0016266324030109","url":null,"abstract":"<p> It is shown how certain recent results in the theory of determinants and traces can be applied to obtain new theorems on the distribution of eigenvalues of nuclear operators on Banach spaces and to prove the equality of the spectral and nuclear traces of such operators. As an example, we consider a new class of operators: the class of generalized Lapresté nuclear operators. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"344 - 346"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434884","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
Inverse Problem for the (L)-Operator in the Lax Pair of the Boussinesq Equation on the Circle 圆上布森斯方程的拉克斯对中的（L）-操作者的逆问题
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030092
Andrey Badanin, Evgeny Korotyaev
{"title":"Inverse Problem for the (L)-Operator in the Lax Pair of the Boussinesq Equation on the Circle","authors":"Andrey Badanin,&nbsp;Evgeny Korotyaev","doi":"10.1134/S0016266324030092","DOIUrl":"10.1134/S0016266324030092","url":null,"abstract":"<p> We consider a third-order non-self-adjoint operator which is an <span>(L)</span>-operator in the Lax pair for the Boussinesq equation on the circle. We construct a mapping from the set of operator coefficients to the set of spectral data, similar to the corresponding mapping for the Hill operator constructed by E. Korotyaev. We prove that, in a neighborhood of zero, our mapping is analytic and one-to-one. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"340 - 343"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434942","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 Local Everywhere Hölder Continuity of the Minima of a Class of Vectorial Integral Functionals of the Calculus of Variations 论变分法一类矢量积分函数最小值的局部无处不在的荷尔德连续性
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030031
Tiziano Granuzzi
{"title":"On the Local Everywhere Hölder Continuity of the Minima of a Class of Vectorial Integral Functionals of the Calculus of Variations","authors":"Tiziano Granuzzi","doi":"10.1134/S0016266324030031","DOIUrl":"10.1134/S0016266324030031","url":null,"abstract":"<p> In this paper we study the everywhere Hölder continuity of the minima of the following class of vectorial integral funcionals: </p><p> with some general conditions on the density <span>(G)</span>. </p><p> We make the following assumptions about the function <span>(G)</span>. Let <span>(Omega)</span> be a bounded open subset of <span>(mathbb{R}^{n})</span>, with <span>(ngeq 2)</span>, and let <span>(G colon Omega timesmathbb{R}^{m}timesmathbb{R}_{0,+}^{m}to mathbb{R})</span> be a Carathéodory function, where <span>(mathbb{R}_{0,+}=[0,+infty))</span> and <span>(mathbb{R} _{0,+}^{m}=mathbb{R}_{0,+}times dots timesmathbb{R}_{0,+})</span> with <span>(mgeq 1)</span>. We make the following growth conditions on <span>(G)</span>: there exists a constant <span>(L&gt;1)</span> such that </p><p> for <span>(mathcal{L}^{n})</span> a.e. <span>(xin Omega )</span>, for every <span>(s^{alpha}in mathbb{R})</span> and every <span>(xi^{alpha}inmathbb{R})</span> with <span>(alpha=1,dots,m)</span>, <span>(mgeq 1)</span> and with <span>(a(x) in L^{sigma}(Omega))</span>, <span>(a(x)geq 0)</span> for <span>(mathcal{L}^{n})</span> a.e. <span>(xin Omega)</span>, <span>(sigma &gt;{n}/{p})</span>, <span>(1leq q&lt;{p^{2}}/{n})</span> and <span>(1&lt;p&lt;n)</span>. </p><p> Assuming that the previous growth hypothesis holds, we prove the following regularity result. If <span>(u,{in}, W^{1,p}(Omega,mathbb{R}^{m}))</span> is a local minimizer of the previous functional, then <span>(u^{alpha}in C_{mathrm{loc}}^{o,beta_{0}}(Omega) )</span> for every <span>(alpha=1,dots,m)</span>, with <span>(beta_{0}in (0,1) )</span>. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude Hölder continuity. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"251 - 267"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434937","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
Quasiderivations of the Algebra (Umathfrak{gl}_n) and the Quantum Mischenko–Fomenko Algebras 代数（Umathfrak{gl}_n）和量子 Mischenko-Fomenko 代数的类iderivations
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030080
Georgii Sharygin
{"title":"Quasiderivations of the Algebra (Umathfrak{gl}_n) and the Quantum Mischenko–Fomenko Algebras","authors":"Georgii Sharygin","doi":"10.1134/S0016266324030080","DOIUrl":"10.1134/S0016266324030080","url":null,"abstract":"<p> Quasiderivations of the universal enveloping algebra <span>(Umathfrak{gl}_n)</span> were first introduced by D. Gurevich, P. Pyatov, and P. Saponov in their study of reflection equation algebras; they are linear operators on <span>(Umathfrak{gl}_n)</span> that satisfy certain algebraic relations, which generalise the usual Leibniz rule. In this note, we show that the iterated action of the operator equal to a linear combination of the quasiderivations on a certain set of generators of the center of <span>(Umathfrak{gl}_n)</span> (namely on the symmetrised coefficients of the characteristic polynomial) produces commuting elements. The resulting algebra coincides with the quantum Mischenko–Fomenko algebra in <span>(Umathfrak{gl}_n)</span>, introduced earlier by Tarasov, Rybnikov, Molev, and others. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"326 - 339"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434939","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
Flat Hypercomplex Nilmanifolds are (mathbb H)-Solvable 平超复数无穷折线是（mathbb H ）可解的
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S001626632403002X
Yulia Gorginyan
{"title":"Flat Hypercomplex Nilmanifolds are (mathbb H)-Solvable","authors":"Yulia Gorginyan","doi":"10.1134/S001626632403002X","DOIUrl":"10.1134/S001626632403002X","url":null,"abstract":"<p> Let <span>(mathbb H)</span> be a quaternion algebra generated by <span>(I,J)</span> and <span>(K)</span>. We say that a hypercomplex nilpotent Lie algebra <span>(mathfrak g)</span> is <span>(mathbb H)</span><i>-solvable</i> if there exists a sequence of <span>(mathbb H)</span>-invariant subalgebras containing <span>(mathfrak g_{i+1}=[mathfrak g_i,mathfrak g_i])</span>, </p><p> such that <span>([mathfrak g_i^{mathbb H},mathfrak g_i^{mathbb H}]subsetmathfrak g^{mathbb H}_{i+1})</span> and <span>(mathfrak g_{i+1}^{mathbb H}=mathbb H[mathfrak g_i^{mathbb H},mathfrak g_i^{mathbb H}] )</span>. Let <span>(N=Gammasetminus G)</span> be a hypercomplex nilmanifold with the flat Obata connection and <span>(mathfrak g=operatorname{Lie}(G))</span>. We prove that the Lie algebra <span>(mathfrak g)</span> is <span>(mathbb H)</span>-solvable. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"240 - 250"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434936","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 Absence of an Additional Real-Analytic First Integral in the Problem of the Motion of a Dynamically Symmetric Heavy Rigid Body about a Fixed Point 论动态对称重刚体绕定点运动问题中不存在附加实解析第一积分
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030067
Sergei Ziglin
{"title":"On the Absence of an Additional Real-Analytic First Integral in the Problem of the Motion of a Dynamically Symmetric Heavy Rigid Body about a Fixed Point","authors":"Sergei Ziglin","doi":"10.1134/S0016266324030067","DOIUrl":"10.1134/S0016266324030067","url":null,"abstract":"<p> We consider the problem of the motion of a dynamically symmetric heavy rigid body about a fixed point and give a detailed proof that the problem has no additional real-analytic first integral in all but the well-known classical cases. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"299 - 312"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434935","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 Extrema of (q)- and Dual (q)-Quermassintegrals for the Asymmetric (L_p)-Difference Bodies 不对称(L_p)-差分体的(q)-和双(q)-质点积分的极值
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI: 10.1134/S0016266324030018
Weidong Wang,  Hui Xue
{"title":"The Extrema of (q)- and Dual (q)-Quermassintegrals for the Asymmetric (L_p)-Difference Bodies","authors":"Weidong Wang,&nbsp; Hui Xue","doi":"10.1134/S0016266324030018","DOIUrl":"10.1134/S0016266324030018","url":null,"abstract":"<p> Wang and Ma introduced the notion of asymmetric <span>(L_p)</span>-difference bodies. They further gave the extrema of volumes for the asymmetric <span>(L_p)</span>-difference body and its polar. Thereafter, Shi and Wang obtained their versions of quermassintegrals and dual quermassintegrals. In this paper, we determine the extrema of the <span>(q)</span>-quermassintegrals and dual <span>(q)</span>-quermassintegrals for the asymmetric <span>(L_p)</span>-difference bodies. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"229 - 239"},"PeriodicalIF":0.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434934","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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