The Expansion Theorem for Pseudo-analytic Functions1 Shmuel Agmon and Lipman Bers

On Rings of Analytic Functions

Let D be a domain in the complex plane (Riemann sphere) and R(D) the totality of one-valued regular analytic functions defined in D. With the usual definitions of addition and multiplication R(D) becomes a commutative ring (in fact, a domain of integrity). A oneto-one conformai transformation f =0(z) of D onto a domain A induces an isomorphism ƒ—>ƒ* between R(D) and R(A):f(z) =ƒ*[(2)]. An an...

Quasiconformal Mappings, with Applications to Differential Equations, Function Theory and Topology by Lipman Bers

The theory of quasiconformal mappings is nearly 50 years old (see [44] for references to the papers by Grötzsch, Ahlfors Lavrent'ev and Morrey from the 20's and 30's) and the interest in them does not seem to wane. These mappings may be studied for their own sake or as a tool for attacking other mathematical problems; they are indeed a powerful and flexible tool. The purpose of this lecture is ...

Mathema Tics: L. Bers

Simultaneous Uniformization by Lipman Bers

We shall show that any two Riemann surfaces satisfying a certain condition, for instance, any two closed surfaces of the same genus g > l , can be uniformized by one group of fractional linear transformations (Theorem 1). This leads, in conjunction with previous results [2; 3] , to the simultaneous uniformization of all algebraic curves of a given genus (Theorems 2-4). Theorem 5 contains an app...

Maximum Theorems for Solutions of Higher Order Elliptic Equations by Shmuel Agmon

The classical maximum modulus theorem for solutions of second order elliptic equations was recently extended by C. Miranda [4] to the case of real higher order elliptic equations in two variables. Previously Miranda [3] has derived a maximum theorem for solutions of the biharmonic equation in two variables. In the case of more variables it was observed by Agmon-Douglis-Nirenberg [2 ] that a max...