Siberian Mathematical Journal最新文献

We consider Kolmogorov operators with constant diffusion matrices and linear drifts, i.e.,Ornstein–Uhlenbeck operators, and show thatall solutions to the corresponding stationary Fokker–Planck–Kolmogorov equations (including signed solutions)are invariant measures for the generated semigroups. This also gives a relatively explicit description of all solutions.

Considering the approximation of a function ( f ) from a Sobolev spaceby the partial sums of Fourier series in a system of Sobolev orthogonal polynomialsgenerated by classical Laguerre polynomials,we obtain an estimate for the convergence rate of the partial sums to ( f ).

We study admissible rulesfor the extensions of the modal logics S4and GLwith the weak co-covering propertyand describe some explicit independent basis for the admissible rules of these logics.The resulting basis consists of an infinite sequence of rulesin compact and simple form.

We construct some class of selfadjoint operators in the Krein spaces consisting of functions onthe straight line ( {operatorname{Re}s=frac{1}{2}} ).Each of these operators is a rank-one perturbation of a selfadjoint operatorin the corresponding Hilbert spaceand has eigenvalues complex numbers of the form ( frac{1}{s(1-s)} ),where ( s ) ranges over the set of nontrivial zeros of the Riemann zeta-function.

We fully study the oriented rotatability exponents of solutions tohomogeneous autonomous linear differential systems andestablish that the strong and weak orientedrotatability exponents coincide for each solution to an autonomous systemof differential equations. We also show that thespectrum of this exponent (i.e., the set of values of nonzerosolutions) is naturally determined by the number-theoreticproperties of the set of imaginary parts of the eigenvalues of thematrix of a system. This set (in contrast to the oscillationand wandering exponents) can contain other than zero values and theimaginary parts of the eigenvalues of the system matrix; moreover,the power of this spectrum can be exponentially large incomparison with the dimension of the space.In demonstration we use the basics of ergodic theory,in particular, Weyl’s Theorem.We prove that the spectra of all oriented rotatability exponentsof autonomous systems with a symmetricalmatrix consist of a single zero value.We also establish relationshipsbetween the main values of the exponents on a set of autonomous systems.The obtained results allow us to conclude that the exponents oforiented rotatability, despite their simple and natural definitions,are not analogs of the Lyapunov exponent in oscillation theory.

A topological fibered space is a Birman–Hilden spacewhenever in each isotopic pair of its fiber-preserving(taking each fiber to a fiber) self-homeomorphismsthe homeomorphisms are also fiber-isotopic(isotopic through fiber-preserving homeomorphisms).We present a series of sufficient conditionsfor a fiber bundle over the circleto be a Birman–Hilden space.

We prove the equivalence of the power-law convergence rate in the ( L_{2} )-normof ergodic averages for ( {𝕑}^{d} ) and ( {𝕉}^{d} ) actions and the samepower-law estimate for the spectral measure of symmetric ( d )-dimensionalparallelepipeds: for the degrees that are roots of some special symmetricpolynomial in ( d ) variables. Particularly, all possible rangeof power-law rates is covered for ( d=1 ).

We construct an additive basis for a relatively freealternative algebra of Lie-nilpotent degree 5,describe the associative center and core of this algebra, and findthe T-generators of the full center.Also, we give some asymptotic estimate for the codimensionof the T-ideal generated by a commutator of degree 5in a free alternative algebra, and finda finite-dimensional superalgebra thatgenerates the variety of alternative algebraswith the Lie-nilpotency of the selfadjoint operator of degree 5.

Abstract

Studying the approximation properties of a certain Riesz–Zygmund sum of Fourier–Chebyshev rational integral operators with constraints on the number of geometrically distinct poles, we obtain an integral expression of the operators. We find upper bounds for pointwise and uniform approximations to the function ( |x|^{s} ) with ( sin(0,2) ) on the segment ( [-1,1] ) , an asymptotic expression for the majorant of uniform approximations, and the optimal values of the parameter of the approximant providing the greatest decrease rate of the majorant. We separately study the approximation properties of the Riesz–Zygmund sums for Fourier–Chebyshev polynomial series, establish an asymptotic expression for the Lebesgue constants, and estimate approximations to ( fin H^{(gamma)}[-1,1] ) and ( gammain(0,1] ) as well as pointwise and uniform approximations to the function  ( |x|^{s} ) with ( sin(0,2) ) .

Abstract

We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces. We present the basic techniques of studying these objects as well as the Boolean valued approach to injective Banach lattices.