Boundary interpolation in the ball

We solve a boundary interpolation problem in the reproducing kernel Hilbert space of functions analytic in the unit ball of with reproducing kernel 1/(1−∑₁^Nz_kw_k^*). We introduce the notion of Brune factor (or Blaschke–Potapov factor of the third kind) in this setting.     

ON THE BOUNDEDNESS OF SPHERES IN F-SPACES

In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the F*-space are presented. Moreover, some results about the compactness are also given.     

Stereoelectronic structure of MCl4-benzoyl chloride (M=Si,Ge, Sn) systems resulting from ab initio calculations and NQR 35Cl

Results of quantum-chemical calculations of MCl₄–C₆H₅COCl (M=Si, Ge, Sn) systems of 1?:?1 composition using RHF/3-21?G* and MP2/3-21?G* levels as well as those of 1?:?2 composition using the RHF/3-21?G* level have been represented. MCl₄?←?C₆H₅COCl complexes of 1?:?1 composition are energetically more advantageous. They are formed in solid state provided that the M···O distance in individual systems is considerably less than the sum of van der Waals radii of M and O and their total energies are appreciably less than the sum of total energies of components. These conditions are realized only for M=Sn. In systems of 1?:?2 compositions, calculated M···O distances are practically equal to the sum of covalent radii of M and O. Nonetheless, complexes with such composition are not formed in solid state. Total energy of the system which is lower than the sum of its components’ energies is not an indispensable condition for complex formation. The ³⁵Cl nuclear quadrupole resonance (NQR) frequencies and asymmetry parameters of the electric field gradient at the ³⁵Cl nuclei have been evaluated using the results of ab initio calculations.     

Statistical stationary states for a two-layer quasi-geostrophic system

Existence of a family of locally invariant probability measures for large scale flows in enclosed temperate sea is proved. This model is extremely important for understanding the meso-scale phenomena in oceans. The techniques used are those developed by Albeverio and his collaborators.     

基本的弱正则*-半群的结构

本文给出了基本的弱正则＊－半群的一个结构定理．作为这一结构定理的特 殊情形，基本的正则＊－半群的一个新的结构被给出．     

Mixed multiplicities,Hilbert polynomials and homaloidal surfaces

We investigate the relationship among several numerical invariants associated to a (free) projective hypersurface V : the sequence of mixed multiplicities of its Jacobian ideal, the Hilbert polynomial of its Milnor algebra, and the sequence of exponents when V is free. As a byproduct, we obtain explicit equations for some of the homaloidal surfaces in the projective 3‐dimensional space constructed by C. Ciliberto, F. Russo and A. Simis.     

Nonasymptotic analysis of robust regression with modified Huber's loss

To achieve robustness against the outliers or heavy-tailed sampling distribution, we consider an Ivanov regularized empirical risk minimization scheme associated with a modified Huber's loss for nonparametric regression in reproducing kernel Hilbert space. By tuning the scaling and regularization parameters in accordance with the sample size, we develop nonasymptotic concentration results for such an adaptive estimator. Specifically, we establish the best convergence rates for prediction error when the conditional distribution satisfies a weak moment condition.     

Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc

In [4], Agler and McCarthy (2005) used Hilbert function spaces to study the uniqueness properties of the Nevanlinna-Pick problem on the bidisc. In this work we give a geometric procedure for constructing a Nevanlinna-Pick problem on Dn with a specified set of uniqueness. On the way to establishing this procedure, we prove a result about Hilbert function spaces and partially answer a question posed by Agler and McCarthy.     

Spaces of idempotent measures of compact metric spaces

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.     

Coherent trace-class operators in Hilbert couples

In this paper it is proved that the ideal of trace-class operators acting in a couple of Hilbert spaces coincides with the ideal of coherent trace-class operators. A new formula is derived for theK-functional in the couple of algebras of all bounded linear operators acting in a Hilbert couple, and new interpolation theorems are proved for trace class operators.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 866–872, June, 1998.This research was partially supported by the International Science Foundation and the Russian Government under grant JD 7100.