Approximation of locally integrable functions on the real line

On the approximation of square-integrable functions by exponential series

The expans ion o f a real s q u a r e i n t e g r a b l e f u n c t i o n in a Legendre series is c o n s i d e r e d . Ex i s t ence of best a p p r o x i m a t i o n s f r o m d i f f e r en t sets o f e x p o n e n t i a l func t ions and thei r m e a n c o n v e r g e n c e to the f u n c t i o n in q u e s t i o n are p roved . As an ex t ens ion o f this resul t ex i s t ence a nd m e a n...

Beyond the locally treelike approximation for percolation on real networks.

Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally treelike ansatz. Such an approximation, however, holds only to a limited extent, because real graphs are often characterized by high frequencies of short loops. We present here a theoretical framework able to overcome such a limitation for the case of site percolation. Our ...

On Approximation of Continuous Functions by Entire Functions of Exponential Type on Subsets of the Real Line

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type on unbounded closed proper subsets of the real line is studded.

On Padé Approximation of Some Practical Functions

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators. r 2004 Elsevier Inc. All rights reserved.