On the absolute Riesz summability of orthogonal series

- , [4]. , .     

Weakly compact operators on function spaces

S — E, F — . C(S, E) S E. : C(S, E) F C(S) . , C(S, E) C(S).     

Convergence of series with respect to generalized Haar systems

. . . . , L _p[0, l], 1 >p <, .     

Metric Density and Quasimobius Mappings

We study the notion of -density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between -density and homogeneous density is established. We also characterize -dense spaces as arcwise connected metric spaces in which arcs are the quasimobius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of ⁿ in terms of -density.     

Sur la répartition des valeurs de la fonction d'Euler

Let (x) denote the number of those integers n with (n) x, where denotes the Euler function. Improving on a well-known estimate of Bateman (1972), we show that (x)-Ax R(x), where A=(2)(3)/(6) and R(x) is essentially of the size of the best available estimate for the remainder term in the prime number theorem.     

Fortsetzungssätze und Moduln über Semifields

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Herrn Professor Dr. Frank Terpe zum 60. Geburtstag gewidmet     

On the rate of convergence of an unstable solution of a stochastic differential equation

We study the rate of convergence of the process(tT)/T to the processw(t)/ asT , where(t) is a solution of the stochastic differential equationd(t)=a((t))dt+((t))dw(t) Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1424–1427, October, 1994.     

Lower semicontinuity of attractors of gradient systems and applications

Summary For 0₀, let T(t), t0, be a family of semigroups on a Banach space X with local attractors A. Under the assumptions that T₀(t) is a gradient system with hyperbolic equilibria and T(t) converges to T₀(t) in an appropriate sense, it is shown that the attractors {A, 0₀} are lower-semicontinuous at zero. Applications are given to ordinary and functional differential equations, parabolic partial differential equations and their space and time discretizations. We also give an estimate of the Hausdorff distance between A and A₀, in some examples.Research supported by U.S. Army Research Office DAAL-03-86-K-0074 and the National Science Foundation DMS-8507056.     

Resolvent of the Toeplitz operator may increase arbitrarily fast

It is proved that for every sequence of points _n from the unit circle, _n1, and for an arbitrary sequence of positive numbers A_n, A_n, there exists a continuous real function u, such that for the Toeplitz operator T (acting in the Hardy space H²) with the symbol =e ^iu we have the estimates (T–_nI)^–1>A_n, n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 175–177, 1987.     

Pseudo-mesures p- adiques associées aux fonctions L deQ

It is shown that some standard results concerning the p-adic L- functions, L_p(), ofQ(p-divisibilities of 1/2L_p(, s), and congruences for 1/2L_p(, t)–1/2L_p(, s), s, t_p) are direct consequences of a general structural theorem, based only on the functional properties of the p-adic pseudo-measures and distributions attached to these L_p-functions (essentially the eulerian ones). The method suggests that all such divisibilities and congruences are obtained systematically by this way, and are the best possible (in a standard point of view). In particular, these results improve significantly all the known ones.     

On the bestL p multipoint local approximation

P (f) — , f L ^p - , k . f 02k–2 P (f) 0.     

A generalization of second variation

f p- , l p . p=1 . . p - , f -.     

Differentiation of fractional order onp-groups,approximation properties

G- p- . [5] - (G) L _r(G) (1r<), . . , - . , , , . . , X. , . (. [1], [2] [4]).     

Sharp Nikolskii inequalities with exponential weights

w _a(x)=exp(–x^a), xR, a0. , N _n (a,p,q) — (2), _n P _nw_ap, CN_n(a,p, q)P_nw_aq. , — , {P _n}, .

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This material is based upon research supported by the National Science Foundation under Grant No. DMS-84-19525, by the United States Information Agency under Senior Research Fulbright Grant No. 85-41612, and by the Hungarian Ministry of Education (first author). The work was started while the second author visited The Ohio State University between 1983 and 1985, and it was completed during the first author's visit to Hungary in 1985.     

Criterion for π-supersolvability for finite groups

It is proved that the class of finite -supersolvable groups is precisely the class of all finite -solvable groups with the following property: For each maximal subgroup M of a -solvable group G with index p for some p , there exists a cyclic subgroup S of order p ( ) such that G = MS and S commutes with each element of the Sylow system _M of the subgroup M.Translated from Matematicheskie Zametki, vol. 52, No. 1, pp. 57–61, July, 1992.     

Замечания об ихтерполировании

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Holomorphe Funktionen auf Gebieten über Banach-Räumen zu vorgegebenen Konvergenzradien

Given a function: ₊ on a domain spread over an infinite dimensional complex Banach space E with a Schauder basis such that -log is plurisubharmonic and d (d denotes the boundary distance on ) one can find a holomorphic function f: with _f, where _f is the radius of convergence of f. If, in addition, is locally Lipschitz continuous with constant 1, f can be chosen so that (3M)^–1 _f, where M is the basis constant of E. In the particular case of E= ₁ there are holomorphic functions f on with= _f.     

Abschnittspositive Matrizen und Positivitätsfaktoren in der Limitierungstheorie

Let A and B be normal matrices. In :={x=(x_k) ¦ x_k} we define the order relation _A by x_A0:<=> _k=0 ⁿ a_nkx_k0 (n ). Let T be a row-finite matrix. A is called T-section-positive, if _kt_mkx_ke^(k) _A0 (m ) for x_A0 (see [5]). We study the relation between T-sectional positivity and T-sectional boundedness. An (A,B)-summability factor sequence =(_k) is called positive, if (_kx_k)_B0 for each xc_A with x_A0. For B-section-positive matrices A we give a functional analytic characterization of positive (A,B)-summability factor sequences.

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Die Arbeit entstand während eines vom DAAD unterstützten Forschungsaufenthalts an der Fernuniversität-Gesamthochschule Hagen     

Zum heutigen Stand der nichtlinearen Optimierungstheorie

Zusammenfassung Die einleitenden Überlegungen gelten der Hauptidee desKuhn-Tucker-Theorems. In die erste Gruppe werden die Cutting plane-Methoden eingereiht. Die zweite Gruppe befaßt sich mit den sogenannten Kleinen-Schritt-Verfahren. Die dritte Gruppe enthält die bekannten Großen-Schritt-Verfahren. In der vierten Gruppe werden die Inneren-Punkt-Verfahren behandelt. Abschließend werden noch einige neuere Methoden vom praktischen und theoretischen Standpunkt aus kurz beleuchtet.

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Summary The introduction is concerned with theKuhn-Tucker theorem. Then the following methods are discussed: cutting plane, small step and large step methods, then the interior point methods. Finally some new methods are studied from the practical and theoretical point of view.

     

On the convergence of Fourier series in the metric ofL 1

L ¹ .