On the Uniqueness of the Recovery of Parameters of the Maxwell System from Dynamical Boundary Data

The paper deals with the problem of recovering the parameters (functions) and of the Maxwell dynamical system

Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences

§ 1　 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0 0 (…     

Homogenization of two-phase metrics and applications

We consider two-phase metrics of the form ϕ(x, ξ) ≔ , where α,β are fixed positive constants and B _α, B _β are disjoint Borel sets whose union is ℝ^N, and prove that they are dense in the class of symmetric Finsler metrics ϕ satisfying

Problems on Extremal Decomposition of the Riemann Sphere

We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let be a system of distinct points on and let be the family of all systems of nonoverlapping simply connected domains on such that . Let

On One Extremal Problem for a Seminorm on the Space l<Subscript>1</Subscript> with Weight

Let be a nondecreasing sequence of positive numbers and let l _1,α be the space of real sequences for which . We associate every sequence ξ from l _1,α with a sequence , where ϕ(·) is a permutation of the natural series such that , j ∈ ℕ. If p is a bounded seminorm on l _1,α and , then

On the decay rate of (p, A)-lacunary series

A power series with radius of convergence equal 1 is called a (p,A)-lacunary one if n_k ≥ Ak^p, A > 0, 1 < p < ∞. It is proved that if 1 < p < 2 and f(x) is a (p,A)-lacunary series that satisfies the condition

Rauzy tilings and bounded remainder sets on the torus

For the two-dimensional torus , we construct the Rauzy tilings d⁰ ⊃ d¹ ⊃ … ⊃ d^m ⊃ …, where each tiling d^m+1 is obtained by subdividing the tiles of d^m. The following results are proved. Any tiling d^m is invariant with respect to the torus shift S(x) = x+ mod ℤ², where ζ⁻¹ > 1 is the Pisot number satisfying the equation x³− x²−x-¹ = 0. The induced map is an exchange transformation of B^md ⊂ , where d = d⁰ and . The map S^(m) is a shift of the torus , which is affinely isomorphic to the original shift S. This means that the tilings d^m are infinitely differentiable. If Z_N(X) denotes the number of points in the orbit S¹(0), S²(0), …, S^N(0) belonging to the domain B^md, then, for all m, the remainder r_N(B^md) = Z_N(B^md) − N ζ^m satisfies the bounds −1.7 < r_N(B^md) < 0.5. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 83–106.     

Carleson measures and the heat equation

Let { }, where { } is the open unit disk on the complex plane { }. In G, we consider analytic solutions u(t, z) ({ }, { }) of the heat equation 2u_t=u_zz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have { } Bibliography: 17 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155. Translated by S. V. Kislyakov.     

Effects Connected with the Coincidence of Velocities in the Two-Velocity Dynamical System

The paper deals with the system

On the Lax Solution to the Hamilton–Jacobi Equation and Its Generalizations. Part II

This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])

On the Littlewood-Paley theorem for arbitrary intervals

We extend the results of Rubio de Francia and Bourgain by showing that, for arbitrary mutually disjoint intervals Δ_k ⊂ ℤ₊, arbitrary p ∈, (0, 2], and arbitrary trigonometric polynomials f _k with supp , we have

On Epstein's Zeta-Function

Let , and let be Epstein's zeta-function of the form Q. It is proved that for |t| > C > 0 one has the estimate

Energy transfer in the Kuramoto-Sivashinskii equation on a multidimensional torus with Riemannian metric

In this paper, we consider the Kuramoto-Sivashinskii equation on the multidimensional torus with a Riemannian metric: where . For this equation the theorem on energy transfer holds. It is formulated in the following way. Let be the Fourier expansion of the function u. Denote by P _N and P _N ^⊥ the operators of rejection of the “leading” and, respectively, “lowest” terms of the Fourier expansion (harmonics), i.e., . For any ρ > 0,N ∈ ℕ, s ≥ n/2+5, and λ ∈ (0, 1), there exists R such that for any function. ϕ ∈ lying outside the ball in the ball , there exists an instant of time t ∈ (0, 1) such that g _KS ^t ϕ=ψ and . Here, R is a constant depending on the metric (g), n _s is the sth Sobolev norm, and is the C ¹-norm. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical Systems and Optimization, 2005.     

Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes

In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.     

Characterizations of Hardy-Orlicz and Bergman-Orlicz spaces

Let and τ denote the invariant gradient and invariant measure on the unit ball B of ℂⁿ, respectively. Assume that f is a holomorphic function on B and ϕ ∈ C²(ℝ) is a nonnegative, nondecreasing, convex function. Then f belongs to the Hardy-Orlicz space H _ϕ(B>) if and only if

Class Numbers of Indefinite Binary Quadratic Forms

Let be the class number of properly equivalent primitive binary quadratic forms of discriminant . The case of indefinite forms is considered. Assuming that the extended Riemann hypothesis for some fields of algebraic numbers holds, the following results are proved. 1. Let be an arbitrarily slow monotonically increasing function such that . Then

Monotonicity of Average Power Means

A new numerical inequality for average power means is presented. Let and let be a sequence of positive numbers. Consider the operator . We denote by the superposition of these operators. The following assertion is proved: if . Bibliography: 2 titles.     

Boundary functions in L2 H $$(\mathbb{B}^n )$$

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball For a function u which is lower semi-continuous on we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈ such that