Bounded approximation by analytic functions

Approximation of Analytic Functions by Chebyshev Functions

and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...

Approximation of Analytic Functions by Special Functions

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

Approximation of Analytic Functions by Kummer Functions

Bounded Analytic Functions

If D is a domain in the complex s-plane, then the family B=B(D) of bounded analytic functions in D is defined as consisting of those analytic functions ƒ(z) which are regular and single-valued in D and which satisfy the inequality \f(z) | < 1 at all points of D. The classical investigations of the family B(D) were restricted to the case in which D is a simply-connected domain. In fact, D was ge...

On Bounded Analytic Functions

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [l] and Garabedian [2].1 While it is admitted that the main idea to be used is more in the nature of a lucky guess than of a method, it will be found that the gain in brevity and simplicity of the argument is considerable. As a by-product, we shall also obtain a...