Universal approximation by systems of hill functions
Universal approximation theorem for Dirichlet series.
Universal approximations of certain functionals in Banach spaces
Universal harmonic functions on the hyperbolic space
We prove universal overconvergence phenomena for harmonic functions on the real hyperbolic space.
Universal Ls-rate-optimality of Lr-optimal quantizers by dilatation and contraction
We investigate in this paper the properties of some dilatations or contractions of a sequence (αn)n≥1 of Lr-optimal quantizers of an -valued random vector defined in the probability space with distribution . To be precise, we investigate the Ls-quantization rate of sequences when or s ∈ (r, +∞) and . We show that for a wide family of distributions, one may always find parameters (θ,µ) such that (αnθ,µ)n≥1 is Ls-rate-optimal. For the Gaussian and the exponential distributions we show...
Universal simultaneous approximations of the coefficient functionals
Universal Taylor series
We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a -dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.
Universally optimal approximation of functionals
A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.
Univerzální diferenciální rovnice (Věnováno památce Waltera Strodta)
Untersuchungen über das Wachstum von Potenzreihenabschnitten mit Anwendungen für das Hornerschema.
Upper and lower estimates for Schauder frames and atomic decompositions
We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite-dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable...
Upper bounds for the norm of Fekete polynomials on subarcs
UR Birkhoff interpolation with rectangular sets of derivatives
In this paper we characterize the regular UR Birkhoff interpolation schemes ( uniform, rectangular sets of nodes) with rectangular sets of derivatives, and beyond.
Used of interpolatory linear positive operators for calculus the moments of the related probability distributions.