Bernstein–Walsh Theory Associated to Convex Bodies and Applications to Multivariate Approximation Theory

Multivariate Approximation: Theory and Applications

A set of irregularly distributed points is fitted to a Least-Squares approximating surface constructed as linear combination of wavelets. The construction proceeds adaptively on a coarse-to-fine refinement. We discuss by numerical experiments the efficiency of the method in relation to iterative solution procedures. Furthermore, we present extensions of the method that allow to cope with wrong ...

"Multivariate Approximation: Theory and Applications"

This introductory paper describes the main topics of this special issue, dedicated to Leonardo Traversoni, known at international level as the promoter of the conference series “Multivariate Approximation: Theory and Applications”, to celebrate his 60th birthday.

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

Optical Elastography: From Theory to Clinical Applications

Logarithmic Potential Theory with Applications to Approximation Theory

We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete points, logarithmic capacity, and Chebyshev constant through a variety of examples and exercises. Many of the fundamental theorems of potential theory, such as Fr...