This is an announcement for the paper "Some classes of rational functions and related Banach spaces" by R. M. Dudley, Sergiy Sidenko, Zuoqin Wang, and Fangyun Yang.

Abstract: For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded above by M and below by 1/M. Each numerator is a monic monomial of the same degree as the corresponding denominator. Then we form the Banach space of countable linear combinations of such rational functions with absolutely summable coefficients, normed by the infimum of sums of absolute values of the coefficients. We show that for rational functions whose denominators are rth powers of a specific 1+Q, or differences of two such rational functions with the same numerator, the norm is achieved by and only by the obvious combination of one or two functions respectively. We also find bounds for coefficients in partial-fraction decompositions of some specific rational functions, which in some cases are quite sharp.

Archive classification: math.FA

Mathematics Subject Classification: 46B99 (primary), 46B22 (secondary)

Remarks: LaTex, 18 pages, no figures

The source file(s), bspsrtlfncts.tex: 74856 bytes, is(are) stored in gzipped form as 0709.2449.gz with size 25kb. The corresponding postcript file has gzipped size 93kb.

Submitted from: rmd@math.mit.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0709.2449

or

http://arXiv.org/abs/0709.2449

or by email in unzipped form by transmitting an empty message with subject line

uget 0709.2449

or in gzipped form by using subject line

get 0709.2449

to: math@arXiv.org.