Numerical peak points and numerical Šilov boundary for holomorphic functions

Norm and Numerical Peak Holomorphic Functions on Banach Spaces

We introduce the notion of numerical (strong) peak function and investigate the denseness of the norm and numerical peak functions on complex Banach spaces. Let Ab(BX : X) be the Banach space of all bounded continuous functions f on the unit ball BX of a Banach space X and their restrictions f |B◦ X to the open unit ball are holomorphic. In finite dimensional spaces, we show that the intersecti...

Denseness of Numerical Radius Attaining Holomorphic Functions

LetX be a complex Banach space andX∗ its dual space. We consider the topological subspace Π X { x, x∗ : x∗ x 1 ‖x‖ ‖x∗‖} of the product space BX ×BX∗ , equipped with norm and weak-∗ topology on the unit ball BX ofX and its dual unit ball BX∗ , respectively. It is easy to see that Π X is a closed subspace of BX × BX∗ . For two complex Banach spaces X and Y , denote by Cb BX : Y the Banach space ...

Multiplicities, Boundary Points, and Joint Numerical Ranges

The multiplicity of a point in the joint numerical range W (A1, A2, A3) ⊆ R is studied for n×n Hermitian matrices A1, A2, A3. The relative interior points of W (A1, A2, A3) have multiplicity greater than or equal to n−2. The lower bound n−2 is best possible. Extreme points and sharp points are studied. Similar study is given to the convex set V (A) := {xT Ax : x ∈ R, x x = 1} ⊆ C, where A ∈ Cn×...

Numerical analytic continuation of holomorphic functions in Cn

‎A Consistent and Accurate Numerical Method for Approximate Numerical Solution of Two Point Boundary Value Problems

In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...