• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
Of all publications in the section: 153
Sort:
by name
by year
Article
Akbarov S. S. Functional Analysis and Its Applications. 2000. Vol. 34. No. 1. P. 60-63.
Added: Sep 23, 2016
Article
V. V. Lebedev. Functional Analysis and Its Applications. 2012. Vol. 46. No. 2. P. 121-132.

We obtain a partial solution of the problem on the growth of the norms of exponential functions with a continuous phase in the Wiener algebra. The problem was posed by J.-P. Kahane at the International Congress of Mathematicians in Stockholm in 1962. He conjectured that (for a nonlinear phase) one can not achieve the growth slower than the logarithm of the frequency. Though the conjecture is still not confirmed, the author obtained first nontrivial results. 

Added: Oct 2, 2012
Article
Schwarzman O., Vinberg E. Functional Analysis and Its Applications. 2017. Vol. 51. No. 1. P. 32-47.

Let Γ be an arithmetic group of affine automorphisms of the n-dimensional future tube T. It is proved that the quotient space T/Γ is smooth at infinity if and only if the group Γ is generated by reflections and the fundamental polyhedral cone (“Weyl chamber”) of the group dΓ in the future cone is a simplicial cone (which is possible only for n ≤ 10). As a consequence of this result, a smoothness criterion for the Satake–Baily–Borel compactification of an arithmetic quotient of a symmetric domain of type IV is obtained.

Added: May 17, 2017
Article
Akbarov S. S. Functional Analysis and Its Applications. 2016. Vol. 50. No. 2. P. 143-145.

To an arbitrary involutive stereotype algebra A the continuous envelopeoperation assigns its nearest, in some sense, involutive stereotype algebra EnvCA so that homomorphisms to various C*-algebras separate the elements of EnvC A but do not distinguish between the properties of A and those of EnvCA.

If A is an involutive stereotype subalgebra in the algebra C(M) of continuous functions on a paracompact locally compact topological space M, then, for C(M) to be a continuous envelope of A, i.e., EnvCA = C(M), it is necessary butnot sufficient that A be dense in C(M). In this note we announce a necessary and sufficient condition for this: the involutive spectrum of A must coincide with M up to a weakening of the topology such that the system of compact subsets in M and the topology on each compact subset remains the same.

Added: Sep 23, 2016
Article
Abramov Y. V. Functional Analysis and Its Applications. 2013. Vol. 47. No. 3. P. 82-87.
Explicit expressions for polynomials forming a homogeneous resultant system of a set of m+1 homogeneous polynomial equations in n+1
Added: Nov 20, 2012
Article
V. V. Lebedev. Functional Analysis and Its Applications. 2017. Vol. 51. No. 2. P. 148-151.

It is well--known that certain properties of continuous functions on the circle T, related to the Fourier expansion, can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the results in this area is the Jurkat--Waterman theorem on conjugate functions, which improves the classical Bohr--P\'al theorem.  In the present work we propose a short and technically very simple proof of the Jurkat--Waterman theorem. Our approach yields a stronger result.

Added: Jun 29, 2017
Article
Protasov V. Y. Functional Analysis and Its Applications. 2013. Vol. 47. No. 2. P. 138-147.

Asymptotic properties of products of random matrices ξ k = X k …X 1 as k → ∞ are analyzed. All product terms X i are independent and identically distributed on a finite set of nonnegative matrices A = {A 1, …, A m }. We prove that if A is irreducible, then all nonzero entries of the matrix ξ k almost surely have the same asymptotic growth exponent as k→∞, which is equal to the largest Lyapunov exponent λ(A). This generalizes previously known results on products of nonnegative random matrices. In particular, this removes all additional “nonsparsity” assumptions on matrices imposed in the literature.We also extend this result to reducible families. As a corollary, we prove that Cohen’s conjecture (on the asymptotics of the spectral radius of products of random matrices) is true in case of nonnegative matrices.

Added: Feb 22, 2016
Article
Makhlin I. Functional Analysis and Its Applications. 2016. Vol. 50. No. 2. P. 98-106.

This work is motivated by the observation that the character of an irreducible gln-module (a Schur polynomial), being the sum of exponentials of integer points in a Gelfand–Tsetlin polytope, can be expressed by using Brion’s theorem. The main result is that, in the case of a regular highest weight, the contributions of all nonsimplicial vertices vanish, while the number of simplicial vertices is n! and the contributions of these vertices are precisely the summands in Weyl’s character formula.

Added: Sep 5, 2016
Article
Бонатти К., Минков С. С., Окунев А. В. и др. Функциональный анализ и его приложения. 2017. Т. 51. № 2. С. 83-86.
Added: Oct 14, 2018
Article
Makhlin I. Functional Analysis and Its Applications. 2015. Vol. 49. No. 1. P. 15-24.

We give an alternative proof of the main result of [1]; the proof relies on Brion’s theorem about convex polyhedra. The result itself can be viewed as a formula for the character of the Feigin-Stoyanovsky subspace of an integrable irreducible representation of the affine Lie algebra widehatsln(C). Our approach is to assign integer points of a certain polytope to vectors comprising a monomial basis of the subspace and then compute the character by using (a variation of) Brion’s theorem.

Added: Aug 7, 2015
Article
Feigin E. Functional Analysis and Its Applications. 2014. Vol. 48. No. 1. P. 59-71.

The degenerate Lie group is a semidirect product of the Borel subgroup with the normal abelian unipotent subgroup. We introduce a class of the highest weight representations of the degenerate group of type A, generalizing the PBW-graded representations of the classical group. Following the classical construction of the flag varieties, we consider the closures of the orbits of the abelian unipotent subgroup in the projectivizations of the representations. We show that the degenerate flag varieties $\Fl^a_n$ and their desingularizations $R_n$ can be obtained via this construction. We prove that the coordinate ring of $R_n$ is isomorphic to the direct sum of duals of the highest weight representations of the degenerate group. In the end, we state several conjectures on the structure of the highest weight representations.

Added: Apr 30, 2014
Article
Ilyashenko Y. Functional Analysis and Its Applications. 2008. No. 42(4). P. 60-71.
Added: Feb 15, 2012
Article
Olshanski G. Functional Analysis and Its Applications. 2016. Vol. 50. No. 3. P. 237-240.

The Thoma cone is a certain infinite-dimensional space that arises in the representation theory of the infinite symmetric group. The present note is a continuation of a paper by A. M. Borodin and the author (Electr. J. Probab. 18 (2013), no. 75), where a 2-parameter family of continuous-time Markov processes on the Thoma cone was constructed. The purpose of the note is to show that these processes are diffusions.

Added: Nov 14, 2016
Article
Artamkin I., Levitskaya Y., Shabat G. B. Functional Analysis and Its Applications. 2009. Vol. 43. No. 2. P. 140-142.

The paper contains an explicit construction of Strebel differentials on one-parameter families of hyperelliptic curves of even genus. Descriptions of the corresponding separatrices are presented.

Added: Jan 25, 2013
Article
Olshanski G. Functional Analysis and Its Applications. 2016. Vol. 50. No. 2. P. 107-130.

The boundary of the Gelfand–Tsetlin graph is an infinite-dimensional locally compact space whose points parameterize the extreme characters of the infinite-dimensional group U(∞). The problem of harmonic analysis on the group U(∞) leads to a continuous family of probability measures on the boundary—the so-called zw-measures. Recently Vadim Gorin and the author have begun to study a q-analogue of the zw-measures. It turned out that constructing them requires introducing a novel combinatorial object, the extended Gelfand–Tsetlin graph. In the present paper it is proved that the Markov kernels connected with the extended Gelfand–Tsetlin graph and its q-boundary possess the Feller property. This property is needed for constructing a Markov dynamics on the q-boundary. A connection with the B-splines and their q-analogues is also discussed.

Added: Sep 12, 2016
Article
Akhmedov E., Shakirov S. Functional Analysis and Its Applications. 2009. Vol. 43. No. 4. P. 245-253.
Added: Feb 26, 2013
Article
Krylov V. Functional Analysis and Its Applications. 2018. Vol. 52. No. 2. P. 113-133.

Let $G$ be a connected reductive algebraic group over $\mathbb{C}$. Let $\Lambda^{+}_{G}$ be the monoid of dominant weights of $G$. We construct the integrable crystals $\mathbf{B}^{G}(\lambda),\ \lambda\in\Lambda^{+}_{G}$, using the geometry of generalized transversal slices in the affine Grassmannian of the Langlands dual group. We construct the tensor product maps $\mathbf{p}_{\lambda_{1},\lambda_{2}}\colon \mathbf{B}^{G}(\lambda_{1}) \otimes \mathbf{B}^{G}(\lambda_{2}) \rightarrow \mathbf{B}^{G}(\lambda_{1}+\lambda_{2})\cup\{0\}$ in terms of multiplication of generalized transversal slices. Let $L \subset G$ be a Levi subgroup of $G$. We describe the restriction to Levi $\operatorname{Res}^G_L\colon\operatorname{Rep}(G)\rightarrow\operatorname{Rep}(L)$ in terms of the hyperbolic localization functors for the generalized transversal slices.

Added: Sep 11, 2018
Article
Ландо С. К. Функциональный анализ и его приложения. 2006. Т. 40. № 1.
Added: Sep 17, 2008
Article
Pushkar P. E. Functional Analysis and Its Applications. 2000. Vol. 34. No. 4. P. 288-292.
Added: Oct 4, 2010
Article
Agranovich M. S. Functional Analysis and Its Applications. 2011. Vol. 45. No. 2. P. 81-98.

We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space Rn. For such problems, equivalent equations on the boundary in the simplest L2-spaces Hs of Sobolev type are derived, which permits one to represent the solutions via surface potentials. We prove a result on the regularity of solutions in the slightly more general spaces Hsp of Bessel potentials and Besov spaces Bsp. Problems with spectral parameter in the system or in the condition on a part of the boundary are considered, and the spectral properties of the corresponding operators, including the eigenvalue asymptotics, are discussed.

Added: Apr 12, 2012
Article
Ilyashenko Y. Functional Analysis and Its Applications. 2012. Vol. 46. No. 4. P. 239-248.

In this paper we study attractors of skew products, for which the following dichotomy is ascertained. These attractors either are not asymptotically stable or possess the following two surprising properties. The intersection of the attractor with some invariant submanifold does not coincide with the attractor of the restriction of the skew product to this submanifold but contains this restriction as a proper subset. Moreover, this intersection is thick on the submanifold, that is, both the intersection and its complement have positive relative measure. Such an intersection is called a bone, and the attractor itself is said to be bony. These attractors are studied in the space of skew products. They have the important property that, on some open subset of the space of skew products, the set of maps with such attractors is, in a certain sense, prevalent, i. e., "big." It seems plausible that attractors with such properties also form a prevalent subset in an open subset of the space of diffeomorphisms.

Added: Feb 11, 2013