On the existence of analytic functions on closed analytic surfaces

On Closed Ideals of Analytic Functions

1. The closed ideals in the algebra A of all continuous functions fieie) on the unit circle X = {eie: 0^.B<2ir] which have analytic extensions/(z), \z\ <1 have been determined by Beurling and independently by Rudin [5] as follows: Let Hx denote the weak* closure [A]* of A as a subset of Laidm), where m denotes the normalized Lebesgue measure dd/2ir on the circle. A function qEHTM is called inne...

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...

On Sandwich theorems for certain classes of analytic functions

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Nevanlinna on Analytic Functions

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...