Estimates in Minkowski's nonhomogeneous conjecture for small dimensions

One gives estimates from above for the nonhomogeneous arithmetic minimum M _n which are better for n, I.I · I0 than the known ones.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 106, pp. 104–133, 1981.     

Parabolic subgroups of the full linear group over a Dedekind ring of arithmetical type

Suppose K is a global field, S a finite set of valuations of K containing all Archimedean valuations, and R the ring of S-integral elements of K. Assume that card S2, R is generated by its invertible elements, and the ideal of R generated by the differences –1 for all invertible coincides with R. Under these assumptions, the parabolic subgroups of GL(n, R) are described. Namely, for each parabolic subgroup P there exists a unique net of ideals of R (Ref. Zh. Mat., 1977, 2A280) such that e()PG(), where G is the net subgroup of () and E() is the subgroup generated by the transvections in G(). It is shown that E() is a normal subgroup of G(). The factor group G(/E()) is studied. The case of the special linear group is also considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 66–79, 1977.In conclusion,the author would like to thank Z. I. Borevich for posing the problem and for his continued interest, and A. A. Suslin for useful discussions leading to simplifications of some of the proofs.     

О лагранжевом интерполировании с узлами в корнях многочленов сонина-маркова

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Net subgroups of Chevalley groups. II. Gauss decomposition

This paper is a continuation of RZhMat 1980, 5A439, where there was introduced the subgroup () of the Chevalley group G(,R) of type over a commutative ring R that corresponds to a net , i.e., to a set =(),, of ideals of R such that ₊ whenever ,,+ . It is proved that if the ring R is semilocal, then () coincides with the group ₀ considered earlier in RZhMat 1976, 10A151; 1977, 10A301; 1978, 6A476. For this purpose there is constructed a decomposition of () into a product of unipotent subgroups and a torus. Analogous results are obtained for sub-radical nets over an arbitrary commutative ring.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 62–76, 1982.In conclusion, the authors would like to thank Z. I. Borevich for his interest in this paper.     

The lower algebraicK-theory of virtually infinite cyclic groups

This paper gives a proof of a conjecture of W.-C. Hsiang for the negativeK-theory of integral grouprings , when the group is a subgroup of a uniform lattice in a Lie group. The authors' earlier paper reduced this result to the very special cases where either is finite or is virtually infinite cyclic. The finite case was done much earlier by Carter extending results of Bass and Murthy. The major work of the present paper consists of proving the conjecture when is virtually infinite cyclic.Both authors were supported in part by the National Science Foundation.     

The Dual of the martingale Hardy space ℋΦ with general Young function Φwith general Young function Φ

[10], ¹ . [4] K _q-, , 1p2 _pp K _q, q=p/p–1)(q=+, p=1 K = ). — p ⊃<<. , , , — , K . , ( ) , q .     

Einschließungsaussagen für gewöhnliche Differentialoperatoren

Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea ₂ and for given functions = we require =C ₀[0, 1] C ₂([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and .     

Transferring estimates for zonal convolution operators

_p - , . Ad- .     

On approximation of functions on the half-line by algebraic polynomials

, . , .     

Жизнь и деятельность яноша Бояи

: . BOLYAI.     

On convergence of function series

, a _n f _n (x) . .     

On the uniform (C, 1)-summability of Fourier series and integrability of series with respect to multiplicative orthonormal systems

H (G), f(g)H (G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp _n=, , ,n .. . , 117 234 . . -      

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

Hardy spaces of predictable martingales

, P _p Q _p .

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This research was partially supported by the Hungarian Scientific Foundation.     

Sharpening of Stečkin's theorem to strong approximation with exponentp

— , B _n , B p1., , p=1 , - . , , , p.     

A chord-stretching map of a convex loop is an isometry

Let ⁿ be n-dimensional Euclidean space, and let : [0, L] ⁿ and : [0, L] ⁿ be closed rectifiable arcs in ⁿ of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C ² curves. In this paper we prove the conjecture in general.     

Orthogonal systems invariant under an automorphism

, , - ( ) . , - , ( ) .     

The Cantor-Lebesgue and Denjoy-Luzin properties for double systems of functions

{ _mn ():, =1, 2, ...}, (X, , ). , ( ) , . { _mn }. . — — ( ) .     

Замечания о порядке погрещности интерполяции

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Intrinsic definition of the Colombeau algebra of generalized functions

— G (), . . . , : , , D()G(), , , G(), , , , — .