RAMPEX - a new spin experiment (presented for HELION97, 20-24 Jan 1997, Kobe, Japan)

RAMPEX - Russian-AMerican Polarization EXperiment - is dedicated to studies of one-spin asymmetries which have twist-3 and also twist-2 origin, in hard and semi-hard inclusive processes on the polarized propane-diol target. A special consideration has been given for the prospects of using polarized 3He target. The studies will be performed at the Serpukhov accelerator at 70 GeV/c (proton beam) and 40 GeV/c (pi- beam).Comment: 8 pages, 1 figur

Approximation of differentiation operator in the space L2 on semiaxis

We establish an upper bound for the error of the best approximation of the first order differentiation operator by linear bounded operators on the set of twice differentiable functions in the space L2 on the half-line. This upper bound is close to a known lower bound and improves the previously known upper bound due to E. E. Berdysheva. We use a specific operator that is introduced and studied in the paper. © Allerton Press, Inc., 2013

Trigonometric polynomials of least deviation from zero in measure and related problems

AbstractWe give a solution of the problem on trigonometric polynomials fn with the given leading harmonic ycosnt that deviate the least from zero in measure, more precisely, with respect to the functional μ(fn)=mes{t∈[0,2π]:|fn(t)|≥1}. For trigonometric polynomials with a fixed leading harmonic, we consider the least uniform deviation from zero on a compact set and find the minimal value of the deviation over compact subsets of the torus that have a given measure. We give a solution of a similar problem on the unit circle for algebraic polynomials with zeros on the circle

On the Best Approximation of the Differentiation Operator

In this paper we give a solution of the problem of the best approximation in the uniform norm of the differentiation operator of order k by bounded linear operators in the class of functions with the property that the Fourier transforms of their derivatives of order n (0 < k <n) are finite measures. We also determine the exact value of the best constant in the corresponding inequality for derivatives