Indépendance conditionnelle et uniformité pour les lois fortes des grands nombres dans les espaces de Banach

Summary A. Beck has given an uniform strong law of large numbers for families of mutually symmetric and uniformly essentially bounded sequences of centered random variables, with values in (k, )—B-convex spaces. We show that, without any limitation on the Banach spaces, the technique used by A. Beck allows to replace, in strong law of large numbers making use of conditions bearing on essential bounds, the hypothesis of independence by an hypothesis called conditional-independence-and-centering, which is weaker than both hypothesis of independence and of mutual symmetry; moreover, in several cases, one gets uniform strong laws of large numbers (for families of conditionally-independent-and-centered sequences). The results we get are compared with recent results of G. Pisier, obtained with type p spaces techniques.     

The Cesàro-Denjoy-Bochner scale of almost periodicity

, —— , . , f, ——, —. .     

On the divergence of certain Hermite-Fejér interpolation

Summary In his paper [1]P. Turán discovers the interesting behaviour of Hermite-Fejér interpolation (based on the ebyev roots) not describing the derivative values at exceptional nodes {_n} _n=1 . Answering to his question we construct such exceptional node-sequence for which the mentioned process is bounded for bounded functions whenever –1<x<1 but does not converge for a suitable continuous function at any point of the whole interval [–1, 1].     

Über Untergruppen Endlicher Algebraischer Gruppen

Let k be a commutative ring, GG finite affine algebraic k-groups, and HH the dual Hopfalgebras of the affine algebras of G resp. G. The main results of this paper are: (I) If k is semilocal (e.g. k a field) there is an H-linear, HH-colinear, unitary, augmented isomorphism HHH H, where HH is the coalgebra belonging to G/G. (II) If the k-submodule of the fixelements of (HH)^* is isomorphic to k (e.g. k principal or semilocal), then HH is a Frobeniusextension of the second kind.     

A Hubert space characterization among function spaces

— [0,1] ,E — - e=1 [0,1]. I — _E =1, E=L ₂ x _e =xL ₂ x E.

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This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund.     

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

Coproducts in the Category <Emphasis Type="Bold">M</Emphasis>κ<Emphasis Type="Bold">Frm</Emphasis>

The purpose of this paper is to study coproducts in the category MFrm (resp. M_cFrm), of metric -frames and uniform (resp. contractive) -frame maps. First, by applying the same technic that was used to find coproducts in Frm, we construct coproducts in the category Frm of -frames and -frame maps. Then, we define a metric diameter on the coproduct in Frm of a family of metric -frames and show that coproduct in Frm preserves metrizability.Mathematics Subject Classifications (2000) 06B23, 06D22, 18A30.     

C 1 changes of variable: Beurling-Helson type theorem and Hörmander conjecture on Fourier multipliers

We prove that if aC ¹ smooth change of variable : generates a bounded composition operatorff° in the spaceA _p()=L ^p ,p2, then is linear (affine).We also prove that for a nonlinearC ¹ mapping , the norms of exponentialse ⁱ as Fourier multipliers inL ^p () tend to infinity (,||). In both results the condition C ¹ is sharp, it cannot be replaced by the Lipschitz condition.     

Theorem on a convergence condition in the spaces

For a given -function (u), a condition on a -function (u) is found such that it is necessary and sufficient for the following to hold: if f_n(x) f(x) and f _n (x)M (n=1, 2, ...) where M>0 is an absolute constant, then f _n (x)–f(x)0(n). An analogous condition for convergence in Orlicz spaces is obtained as a corollary.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 615–626, May, 1977.The author thanks V. A. Skvortsov for his constant attention and guidance on this paper.     

On summability of subsequences of partial sums of trigonometric Fourier series

n- (n1) fL ^p ([–, ] ⁿ ),=1 = (L C) . , , f([–, ] ⁿ ).     

On a theorem of G. Pólya

f(z), :f(n)=0 (n=0, ±1, ±2, ...). ((n)} L _p ,p>1, .     

Presentations for Certain Chevalley Groups

Let G = P SL_n(K), n 3, K a division ring or D_n(K), n 4 or E_n(K), 6 n 8, K a field. Then two types of presentations for G are given. In the first, G is generated by SL₂(K)'s which satisfies relations according to the Dynkin diagram of G. In the second, G is generated by a set {A_i | i I } of Abelian groups, which satisfy relations similar to the root subgroups of G.     

On multivariate polynomialL 2-approximation to zero

, -, [–1,1] L ². - . , .     

On strong summability of polynomial expansions

—.

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Dedicated to Professor L. Leindler on his 50^th birthday     

Monotonicity properties of zeros of generalized Airy functions

Summary We show, among other things, that the positive zeros of a solution ofy +x y=0,y(0)=0 decrease to 1 as increases, 0.

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Sommario Si dimostra, tra l'altro, che gli zeri positivi d'una soiuzione diy +x y=0,y(0)=0 decrescono al limite 1, quando cresce, 0.

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To the memory of Milo Háik

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This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino.     

A generalized Laplace transform of generalized functions

- . . . , .     

Some inequalities of Hardy-Littlewood type

[3] , >0 n ^– a _n , . , . . , .

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant #234.     

Applications of matrix functions

A, ()=0, c(z)- T - TY=AY. A y(t)=y(, t) Ty=y Y(t). - c(T)y=0.     

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