Polynomial approximation of differentiable functions on Banach spaces.
Polynomial approximations and universality
We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...
Polynomial asymptotics and approximation of Sobolev functions
We prove several results concerning density of , behaviour at infinity and integral representations for elements of the space .
Polynomial best constrained degree reduction in strain energy.
Polynomial chaos in evaluating failure probability: A comparative study
Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial...
Polynomial inequalities, functional spaces and best approximation on the real semiaxis with Laguerre weights.
Polynomial inequalities in Banach spaces
We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.
Polynomial inequalities on algebraic sets
We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in (resp. ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.
Polynomial inequalities on general subsets of
Polynomial interpolation and asymptotic representations for zeta functions [Book]
Polynomial two-point expansions.
Polynomials and multilinear mappings in topological vector-spaces
Polynomials as Linear Combinations of Multivariate B-Splines.
Porosity and compacta with dense ambiguous loci of metric projections
Positive approximation and interpolation using compactly supported radial basis functions.
Positive operators and approximation in function spaces on completely regular spaces.
Positivity Zones and Norms of N-fold Convolutions - I
Power Series Equivalent to Rational Functions: A Shifting-Origin Kronecker Type Theorem, and Normality of Padé Tables.
Preconditioners and Korovkin-type theorems for infinite-dimensional bounded linear operators via completely positive maps
The classical as well as noncommutative Korovkin-type theorems deal with the convergence of positive linear maps with respect to different modes of convergence, like norm or weak operator convergence etc. In this article, new versions of Korovkin-type theorems are proved using the notions of convergence induced by strong, weak and uniform eigenvalue clustering of matrix sequences with growing order. Such modes of convergence were originally considered for the special case of Toeplitz matrices and...
Prediction in Orlicz Spaces.