On the divergence of linear summation methods of Fourier series

[0, 1],fL(0,2),

New covering numbers and spectral properties of operators in Banach spaces

, , , . ., . — s- , . , s- (,s- ) ; _n (T), ¦ _l (T)¦¦ ₂ (T)¦...0, T:EE .

Some remarks on Turán's inequality. III: The completion

. 0pq, 1–1/p+1/p0. f(x) — n, [–1,1],

The geodesic “straightest” lines of a nonlinear nonholonomic manifold in E4

The following properties of the geodesic straightest lines of a system of two Monge equations inE ₄ are established:

On local oscillatory integrals with variable Calderón-Zygmund kernels, II

Let , be a real analytic function or a real-C function on ⁿ andk be a variable Calderón-Zygmund kernel. Define the oscillatory singular integral operatorT by

Die Verteilung der schlichten Funktionen in einem Funktionenraum

We consider the set of regular functions H = { f:f = z + ?_{n = 2}^￥ nb_n zⁿ ,|b_n | \leqslant 1} on |z| < 1H = \{ f:f = z + \sum\limits_{n = 2}^\infty {nb_n z^n ,|b_n |{\mathbf{ }} \leqslant 1\} {\mathbf{ }}} on{\mathbf{ }}|z|{\mathbf{ }}< {\mathbf{ }}1 . We construct a Borel measure and a class of outer measures _h onH. With these and _h we show that: (HS)=0 and _h (HS)=0, (S is the set of normed univalent functions). From _h (HS)=0 follows—forh=t —that the Hausdorff—Billingsley-dimension ofHS is zero.     

Perturbation of hamiltonian systems with Keplerian potentials

Supported by Ministero P.I. Gruppo Nazionale Calcolo delle Variazioni (40%)     

On the computation of modules of long quadrilaterals

We study quadrilateralsQ which are given by two intervals on {:Im = 0} and {:Im = 1}, and two Jordan arcs ₁, ₂, in {:0 Im 1} connecting these two intervals. Many practical problems require the determination of the modulem(Q) ofQ, but ifQ is long, i.e., if

Projection minima of a symmetric convex body

R ⁿ n- , : RⁿPRⁿ/ o - . —

Pointwise hereditary majorization and some applications

A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel'sT as well as Kleene/Feferman's) is applied to systems of intuitionistic and classical arithmetic (H andH ^c) in all finite types with full induction as well as to the corresponding systems with restricted induction and^c.

Necessary and sufficient conditions for interpolation with functions having monotoner-th derivatives

,

A class of strongly nonlinear functional differential equations

Let H be a real Hilbert space, :H [0, + ] a proper l.s.c., convex function with L_k:={u H; u² + (u) k} compact for every k > 0, let > 0 be a given constant and . We prove an existence result for strong solutions to a class of functional differential equations of the form

Norm behavior and zero distribution for orthogonal polynomials with nonsymmetric weights

The asymptotic behavior of thenth root of the leading coefficient of orthogonal polynomials on (–,) and the distribution of their zeros is studied for nonsymmetric weights that behave like exp(–2B|x|) whenx>0 and exp(–2Ax ) whenx<0,>AB. These results generalize previous investigations of Rakhmanov and Mhaskar and Saff who handle the symmetric caseA=B.Communicated by Paul Nevai.     

A test of convergence of Fourier series with respect to multiplicative systems,analogous to the Jordan test

, {p _n} _n=0 (p₀=1, _n2 n2). : x f(t) V(G)

On the automorphism groups of algebraic bounded domains

This paper is a part of author's doctoral thesis. It was partially supported by Sonderforschungsbereich 237 Unordnung und große Fluktuatuionen of the Deutsche Forschungsgemeinschaft