Estimates of n-widths of Sobolev's classes on compact globally symmetric spaces of rank one

AbstractEstimates of Kolmogorov's and linear n-widths of Sobolev's classes on compact globally symmetric spaces of rank 1 (i.e. on Sd, Pd(R), Pd(C), Pd(H), P16(Cay)) are established. It is shown that these estimates have sharp orders in different important cases. New estimates for the (p,q)-norms of multiplier operators Λ={λk}k∈N are given. We apply our results to get sharp orders of best polynomial approximation and n-widths

OPTIMAL SK-SPLINE APPROXIMATION OF SOBOLEV’S CLASSES ON THE 2-SPHERE

Abstract The space of-splines is the linear span of shifts of a single kernel. In this article we introduce-splines on. It is shown that, with suitably chosen kernel, the subspace of-splines realizes sharp orders of Kolmogorov’s-widths in different important situations. 1

Approximation of smooth functions on compact two-point homogeneous spaces

Estimates of Kolmogorov $n$-widths $d_n(B_p^r, L^q)$ and linear $n$-widths \da_n(B_p^r, L^q), ($1\leq q\leq \infty$) of Sobolev's classes $B_p^r$, ($r>0$, $1\leq p\leq \infty$) on compact two-point homogeneous spaces (CTPHS) are established. For part of $(p, q)\in[1,\infty]\times[1,\infty]$, sharp orders of $d_n(B_p^r, L^q)$ or \da_n (B_p^r, L^q) were obtained by Bordin, Kushpel, Levesley and Tozoni in a recent paper `` J. Funct. Anal. 202 (2) (2003), 307--326''. In this paper, we obtain the sharp orders of $d_n(B_p^r, L^q)$ and \da_n (B_p^r, L^q) for all the remaining $(p,q)$. Our proof is based on positive cubature formulas and Marcinkiewicz-Zygmund type inequalities on CTPHS

04401 Abstracts Collection -- Algorithms and Complexity for Continuous

From 26.09.04 to 01.10.04, the Dagstuhl Seminar ``Algorithms and Complexity for Continuous Problems\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

B Stars with and without emission lines, parts 1 and 2

The spectra for B stars for which emission lines occur not on the main sequence, but only among the supergiants, and those B stars for which the presence of emission in H ahlpa is considered to be a significant factor in delineating atmospheric structure are examined. The development of models that are compatible with all known facts about a star and with the laws of physics is also discussed

The A-stars: Problems and perspectives. Monograph series on nonthermal phenomena in stellar atmospheres

Normal A type stars, nonradiative heating in A type stars, magnetic Ap stars. The Am stars, the delta Scu stars, A supergiants, peculiar B type stars, and model atmospheres are addressed

Synthetic spectrum methods for three dimensional supernova models.

This dissertation describes some problems associated with synthesizing emergent spectra from three-dimensional supernova envelope models. We confront these problems by developing a three-dimensional implementation of a hybrid Sobolev/Monte Carlo technique. A collection of experiments (extending from the illustrative to the more detailed) are included

Research fellowship for Dr. E.M. Harrell

Issued as Memorandums [nos. 1-2], and Project abstracts [nos. 1-6], Project no. G-37-60