On rational approximation of functions in rearrangement invariant spaces

Approximation by Trigonometric Polynomials in Weighted Rearrangement Invariant Spaces

We investigate the approximation properties of trigonometric polynomials and prove some direct and inverse theorems for polynomial approximation in weighted rearrangement invariant spaces.

Subspaces of Rearrangement-invariant Spaces

We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, oo) which is/7-convex for some/? > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if ...

The Level Function in Rearrangement Invariant Spaces

An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.

On Rational Approximation of Algebraic Functions

We construct a new scheme of approximation of any multivalued algebraic function f(z) by a sequence {rn(z)}n∈N of rational functions. The latter sequence is generated by a recurrence relation which is completely determined by the algebraic equation satisfied by f(z). Compared to the usual Padé approximation our scheme has a number of advantages, such as simple computational procedures that allo...

Approximation by Rational Functions