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Regular version of the site
Of all publications in the section: 174
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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
Article
Vassiliev V. Functional Analysis and Its Applications. 2016. Vol. 50. No. 3. P. 225-227.

A two-sided estimate of local multiplicities of Maxwell sets of isolated singularities of smooth functions is proved. This estimate is sharp for semi-homogeneous functions. 

Added: Nov 14, 2016
Article
Olshanski G., Osinenko A. Functional Analysis and Its Applications. 2012. Vol. 46. No. 4. P. 262-278.
This work is motivated by the problem of harmonic analysis on "big" groups and can be viewed as a continuation of the first author's paper in Functional Anal. Appl. 37 (2003), no. 4, 281-301. Our main result is the proof of the existence of a family of probability distributions with infinite-dimensional support; these distributions are analogs of multidimensional Euler betadistributions that appear in the Selberg integral.
Added: Feb 11, 2013
Article
Minkov S. S., Okunev A. Functional Analysis and Its Applications. 2016. Vol. 50. No. 1. P. 48-53.

We prove that, for any E u ⊕ E cs partially hyperbolic C 2 diffeomorphism, the ω-limit set of a generic (with respect to the Lebesgue measure) point is a union of unstable leaves. As a corollary, we prove a conjecture made by Ilyashenko in his 2011 paper that the Milnor attractor is a union of unstable leaves. In the paper mentioned above, Ilyashenko reduced the local generecity of the existence of a “thick” Milnor attractor in the class of boundary-preserving diffeomorphisms of the product of the interval and the 2-torus to this conjecture.

Added: May 4, 2016
Article
Гуревич В., Буфетов А. И. Функциональный анализ и его приложения. 2008. № 42 (3). С. 75-77.
Added: Oct 6, 2011
Article
Bychkov B. Functional Analysis and Its Applications. 2015. Vol. 49. No. 2. P. 81-85.

The investigation of decompositions of a permutation into a product of permutations satisfying certain conditions plays a key role in the study of meromorphic functions or, equivalently, branched coverings of the 2-sphere; it goes back to A. Hurwitz’ work in the late nineteenth century. In 2000 M. Bousquet-Melou and G. Schaeffer obtained an elegant formula for the number of decompositions of a permutation into a product of a given number of permutations corresponding to coverings of genus 0. Their formula has not been generalized to coverings of the sphere by surfaces of higher genera so far. This paper contains a new proof of the Bousquet-Melou-Schaeffer formula for the case of decompositions of a cyclic permutation, which, hopefully, can be generalized to positive genera. © 2015, Springer Science+Business Media New York.

Added: Sep 3, 2015
Article
Pushkar P. E. Functional Analysis and Its Applications. 2002. Vol. 36. No. 4. P. 321-323.
Added: Oct 4, 2010
Article
V. V. Lebedev. Functional Analysis and Its Applications. 2014. Vol. 48. No. 3. P. 231-234.

We consider bounded analytic functions in domains generated by sets with the Littlewood– Paley property. We show that each such function is an lp-multiplier.

Added: Oct 24, 2014
Article
Semenov P. Functional Analysis and Its Applications. 2017. Vol. 51. No. 4. P. 318-321.

It is shown that a series of recent (2012–2016) generalizations of the notion of contraction (F-contraction, weak F-contraction, etc.) in fact reduce to known notions of contraction (due to Browder, Boyd and Wong, Meir and Keeler, etc.).

Added: Apr 10, 2018
Article
V. V. Lebedev. Functional Analysis and Its Applications. 2013. Vol. 47. No. 1. P. 27-37.

We consider domains D ⊆ ℝn with C1 boundary and study the following question: For what domains D does the Fourier transform 1D of the characteristic function 1D belong to Lp(ℝn)?

Added: Mar 28, 2013
Article
Rybnikov G. Functional Analysis and Its Applications. 2011. Vol. 45. No. 2. P. 137-148.
Added: Dec 19, 2012
Article
Romanov A. Functional Analysis and Its Applications. 2013. Vol. 47. No. 2. P. 160-163.

A relationship is considered between ergodic properties of a discrete dynamical system on a compact metric space Ω and characteristics of companion algebro-topological objects, namely, the Ellis enveloping semigroup E, the Kohler enveloping operator semigroup Γ, and the semigroup G being the closure of the convex hull of Γ in the weak-star topology on the operator space  End C*(Ω). The main results are formulated for ordinary (having metrizable semigroup E) semicascades and for tame dynamical systems determined by the condition card E ≤ c. A classification of compact semicascades in terms of topological properties of the semigroups specified above is given.

Added: Nov 18, 2013
Article
Akbarov S. S. Functional Analysis and Its Applications. 1995. Vol. 29. No. 4. P. 276-279.
Added: Sep 23, 2016
Article
Горинов А. Г. Функциональный анализ и его приложения. 2004. № 38(2). С. 149-150.
Added: Jan 30, 2012
Article
Natanzon S. M. Functional Analysis and Its Applications. 2010. Vol. 44. No. 1. P. 44-58.
Added: Oct 3, 2010
Article
Akbarov S. S. Functional Analysis and Its Applications. 1999. Vol. 33. No. 2. P. 68-73.
Added: Sep 23, 2016
Article
Agranovich M. S. Functional Analysis and Its Applications. 2011. Vol. 45. No. 1. P. 1-12.

We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface S with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces Hs , the simplest L2-spaces of the Sobolev type, with the use of potential type operators on S. We also discuss, first, the regularity of solutions in somewhat more general Bessel potential spaces and Besov spaces and, second, the spectral properties of problems with spectral parameter in the transmission conditions on S, including the asymptotics of the eigenvalues.

Added: Apr 12, 2012
Article
Akbarov S. S. Functional Analysis and Its Applications. 2006. Vol. 40. No. 2. P. 81-90.

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space EM ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the stereotype algebra ℒ (X) of operators on X there exists a unique (up to isomorphism) stereotype space E such that M lies between two natural stereotype tensor products of E by X,

E⊛X⊆M⊆E⊙X.E⊛X⊆M⊆E⊙X.

. As a corollary, we show that if X is a nuclear Fréchet space with a basis, then each Fréchet module M over the stereotype operator algebra ℒ(X) can be uniquely represented as the projective tensor product of X by some Fréchet space E, M=E⊗ˆXM=E⊗^X.

Added: Sep 23, 2016
Article
Feigin E. Functional Analysis and Its Applications. 2012. No. 46 (1). P. 41-52.
Added: Dec 13, 2012
Article
Bezhaeva Z., Oseledets V. I. Functional Analysis and Its Applications. 2010. Vol. 44. No. 2. P. 83-91.
Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for calculating the entropy of an invariant Erdos measure is proposed. It is shown that, for certain values of the Bernulli parameter, the algorithm gives the Hausdorff dimension of an Erdos measure to 15 decimal places.
Added: Apr 12, 2012