Extremal Distances between Sections of Convex Bodies

Let K, D be centrally symmetric convex bodies in Let k < n and let d_k(K, D) be the smallest Banach–Mazur distance between k-dimensional sections of K and D. Define

On the Problem of Maximizing the Product of Powers of Conformal Radii Nonoverlapping Domains

A sharp estimate of the product

Kolmogorov-type inequalities for mixed derivatives of functions of many variables

Let = (₁,...,_d) be a vector with positive components and let D be the corresponding mixed derivative (of order _j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that

Continuity Conditions for a Class of Gaussian Chaos Processes Related to Continuous Additive Functionals of Lévy Processes

Let be sequences of real numbers which are symmetric in k. Let be independent sequences of independent normal random variables with mean zero and variance one. For each fixed choice of we consider

An Elementary Proof of Pólya-Vinogradov's Inequality, II

Let be a primitive character mod k, k > 2. In [1], the following elementary estimate

On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series

For a trigonometric series

Upper Bounds of the Lebesgue Constants for Fourier–Jacobi Series Summation Methods Defined by a Multiplier Function

Let be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators generated by a multiplier matrix defined by the following relations:

Sharp Constants in Inequalities for Intermediate Derivatives (the Gabushin Case)

We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities

A Generalized Measure Concentrated on a Closed Set of Measure Zero

When E is a closed set of measure zero in the dyadic group and the Walsh series satisfies

Galois Cohomology in Degree Three and Homogeneous Varieties

The central result of this paper is the following generalization of a result of the author on products of Severi–Brauer varieties. Let G be a semi-simple linear algebraic group over a field k. Let V be a generalized flag variety under G. Then there exist finite extensions k_i of k for 1im, elements _i in Br k_i and a natural exact sequence

Exact Kolmogorov-Type Inequalities with Bounded Leading Derivative in the Case of Low Smoothness

We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p [1, ], the following unimprovable inequality holds for functions :

The Infimum of the Energy of Unit Vector Fields on Odd-Dimensional Spheres

We construct a one-parameter family of unit smooth vector fieldsglobally defined on the sphere ^2k+1 for k 2, with energyconverging to the energy of the unit radial vector field, which isdefined on the complementary of two antipodal points. So we prove thatthe infimum of the energy of globally defined unit smooth vector fieldsis

Extensions of Vietoris’s inequalities I

Let β ₀=0.308443… denote the Littlewood-Salem-Izumi number, i.e., the unique solution of the equation

Comparison of Exact Constants in Inequalities for Derivatives of Functions Defined on the Real Axis and a Circle

We investigate the relationship between the constants K(R) and K(T), where is the exact constant in the Kolmogorov inequality, R is the real axis, T is a unit circle,

The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization

Let {X _n } _n0 be a Harris recurrent Markov chain with state space E, transition probability P(x, A) and invariant measure , and let f be a real measurable function on E. We prove that with probability one,

The Limit of Lebesgue Constants for Summation Methods of the Fourier―Legendre Series Defined by a Multiplier Function

Let C[-1,1] be the space of continuous functions f:[-1,1] with the uniform norm, let _Pk be the Legendre polynomials such that _Pk (1)=1, and let _J0 be the Bessel function of zero index. We consider sequences of linear operators (summation methods) _Un:C [-1,1] C[-1,1] defined by a multiplier function as follows:

An Extension of a Class of Iterative Procedures for Nonlinear Quasivariational Inequalities

Consider the convergence of the projection methods based on an extension of a special class of algorithms for the approximation--solvability of the following class of nonlinear quasivariational inequality (NQVI) problems: find an element such that and

Interlineation of functions of 2 variables on M (M≥2) lines with the highest algebraic precision

A general algorithm is proposed for constructing interlineation operators , x=(x₁, x₂) with the properties

The type set for some measures on \mathbb{R}^{2n} with n-dimensional support

Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by

Behavior of Automorphic L-Functions at the Center of the Critical Strip

Let be the Hecke eigenbasis of the space of -cusp forms of weight 2. Let p be a prime. Let be the Hecke L-series of form . The following statements are proved: