Analytic functions and Jordan arcs

An Algorithm for Computing Jordan Chains and Inverting Analytic Matrix Functions

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n×n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n+d)× (n+d) linear system, where d is the order of the zero of detA(λ) at λ ...

Quasi-analytic Vectors and Quasi-analytic Functions

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Analytic Functions and Nonsingularity

We will show that every nonsingular complex variety is a manifold in the analytic topology, but we wish to show more – that it has the natural structure of a complex manifold. In order to do this, we will need to introduce additional structure on the analytic topology. To allow for singular points, we give a definition more general than that of complex manifolds, mimicking our definitions from ...

Description of Inverse Polynomial Images which Consist of Two Jordan Arcs with the Help of Jacobi’s Elliptic Functions∗

First we discuss the description of inverse polynomial images of [−1, 1], which consists of two Jordan arcs, by the endpoints of the arcs only. The polynomial which generates the two Jordan arcs is given explicitly in terms of Jacobi’s theta functions. Then the main emphasis is put on the case where the two arcs are symmetric with respect to the real line. For instance it is demonstrated that t...