Geometrical Theory of Analytic Functions

Morse theory for analytic functions on surfaces

In this paper we deal with analytic functions f : S → R defined on a compact two dimensional Riemannian surface S whose critical points are semi degenerated (critical points having a non identically vanishing Hessian). To any element p of the set of semi degenerated critical points Q we assign an unique index which can take the values −1, 0 or 1, and prove that Q is made up of finitely many (cr...

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.

A New Approach to the Theory of Discrete Analytic Functions

Lf(m,n)=f(m,n)+if(m+1,n)+i~f(m+1,n+1)+i3f(m,n+ 1) =o. (1.1) The concept of a discrete analytic function was introduced by Ferrand [l] and many properties of discrete analytic functions were obtained by D&in [2]. A convolution product for discrete analytic functions was defined by DufEn and Duris [3] and an operational calculus was developed by Hayabara [4] and further extended by Deeter and Lor...

Classification Theory for Hardy Classes of Analytic Functions

Model theory of analytic functions: some historical comments

Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie’s proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber’s conjecture for the complex exponential. My goal in this talk is to surve...