The inequality of Ky Fan and related results

In this survey paper, we present refinements, extensions, and variants of the inequality

Analysis of uniform binary subdivision schemes for curve design

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form

Uniformly maldistributed sequences in a strict sense

It is shown that the following three limits

The maximal accuracy of stable difference schemes for the wave equation

We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u _tt =c ² u _xx , given by

Characterization of Besov-Triebel-Lizorkin spaces via approximation by Whittaker's cardinal series and related unconditional Schauder bases

Let

Some boundary-value problems for linear multidimensional second-order hyperbolic equations

For the linear hyperbolic equations

Linearization,trace, and determinant of certain meromorphic operator functions

In this paper operator functions of type

Singular solutions of a transmission problem in plane linear elasticity for wedge-shaped regions

In plane elasticity, when two different wedge-shaped elastic materials (isotropic, homogeneous) are bonded together along a common edge and subject to tractions on the boundary, the stress field will become infinite at the apex. In fact, asymptotically, the displacementu satisfies

Uniform convergence of sums of order statistics to stable laws

Let X ₁, X ₂,... denote an i.i.d. sequence of real valued random variables which ly in the domain of attraction of a stable law Q with index 0<1. under=" a=" von=" mises=" condition=" we=" show=" that=" the=" sum=" of=" order=" statistics=">

Almost sure invariance principles when EX 1 2 =∞

Summary Let {Y _i} be iid with EY ₁=0, EY ₁ ² =1. Let {X_i} be iid normal mean zero, variance one random variables. According to Strassen's first almost sure invariance principle {X _i} and {Y _i} can be reconstructed on a new probability space without changing the distribution of each sequence such that a.s., thus improving on the trivial bound obtainable from the law of the iterated logarithm: a.s. In this work we establish analogous improvements for symmetric {Y _i} in the domain of normal attraction to a symmetric stable law with index 0<<2. (We make this assumption of symmetry in order to avoid messy details concerning centering constants.) Let {X _i} be iid symmetric stable random variables with index 0<<2. Then, for example, hypotheses are stated which imply for a given satisfying 2> that a.s., thus improving on the trivial bound: a.s., >0.This research was supported in part by a National Science Foundation grant, USA     

Коэффициенты рядов Ф урье и класс Липшица

We generalize and sharpen certain results concerning Fourier series from the Lipschitz class. In particular, for sinnx we prove the following: Let ¦b_n¦n^–2L(n) where L(x) is a continuous and slowly oscillating function. Then

Generalized sine equations,II

In this paper we solve the equations

Sharp Kolmogorov-Type Inequalities for Moduli of Continuity and Best Approximations by Trigonometric Polynomials and Splines

In what follows, $C$ is the space of -periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm; is the mth modulus of continuity of a function f with step h and calculated with respect to P; , ( ), ,

An Elementary Approach to an Eigenvalue Estimate for Matrices

A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for every complex matrix satisfies the following eigenvalue estimate:

Strong uniform consistency of nonparametric regression function estimates

Let (X, Y) be a ^dx-valued random vector and let r(t)=E(Y/X=t) be the regression function of Y on X that has to be estimated from a sample (X _i, Y_i), i=1,..., n. We establish conditions ensuring that an estimate of the form

Laplace approximations for sums of independent random vectors

Summary LetX _i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums under the law transformed by the density exp .     

Lo spazio duale di un prodotto di algebre di Boole e le compattificazioni di Stone

Summary This paper is concerned with the Stone space X of a direct product of infinitely many Boolean algebras. In paragraph 2, after recalling that X is the Stone-ech compactification of the sum (disjoint union) of the Stone spaces of the algebras B_i, we exhibit a compactification of which is not a Stone space and we give a method to construct all the «Stone compactifications» of (the corresponding Boolean algebras are easily characterised). In paragraph 3, a set of ultrafilters of B (the «decomposable» ultrafilters) are introduced: this set properly contains , but, as is shown in paragraph 5, there are direct products that admit nondeeomposable ultrafilters (this is the case iff the set {Card B_i: i I } is not bounded by a natural number). In paragraph 4, among other things, we prove, for the set of decomposable ultrafilters, a weak form of countable compactness, in the sense that every countable clopen cover has a finite subcover; then, we deduce that the set of decomposable ultrafilters is pseudocompact, while obviously is not. Lastly, in paragraph 6, we give a second characterisation of the Stone space of B, showing that every ultrafilter of B can be obtained by iterating in a suitable way the procedure which leads to the construction of decomposable ultrafilters.

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Lavoro eseguito nell'ambito dell'attività del Comitato Nazionale per le Scienze Matematiche del C.N.R.     

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

Analytic solution of vector model kinetic equations with constant kernel and their applications

Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations

Tensor sequences and inductive limits with local partition of unity

In this note we characterize those locally convex hulls for which the -tensor product is topologically isomorphic to the locally convex hull for all normed spaces E. By using -sequences in the sense of W.Kaballo and D.Vogt [18] it is shown that is commutable with -tensor products if and only if F admits a local partition of unity. In this paper we give examples of locally convex hulls with local partition of unity. From this one obtains conditions under which the -tensor product of two bornological (DF)-spaces is again a bornological (DF)-space. Applications to sequence spaces are given.