Functions of uniformly bounded characteristic

Some Unsolved Problems on Meromorphic Functions of Uniformly Bounded Characteristic

The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the fsmily of holomorr.hc f11nctonz of bounded mesn oscilltion in R. After a survey some open problems are proposed in contrast with BMOA(R).

Functions of Uniformly Bounded Characteristic on Riemann Surfaces

A characteristic function T(D, w, f) of Shimizu and Ahlfors type for a function / meromorphic in a Riemann surface R is defined, where D is a regular subdomain of R containing a reference point w G R. Next we suppose that R has the Green functions. Letting T(w,f) = Mthdir T{D,w,f), we define / to be of uniformly bounded characteristic in R, f G UBC(i?) in notation, if sup^g/j T(w, f) < oo. We s...

On Meromorphic Functions of Bounded Characteristic

On Graphs with Characteristic Bounded-Width Functions

Graphs can be represented symbolically by the Ordered Binary Decision Diagram (OBDD) of their characteristic Boolean function. The latter is said to have bounded width b if its minimal-size complete OBDD has bounded width b. Bounded-width functions have small OBDDs and allow efficient functional operations. Therefore, they are of interest in the analysis of symbolic graph algorithms. In this pa...

L1 Covering Numbers for Uniformly Bounded Convex Functions

In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the -covering number M(C([a, b], B), ;L1) in terms of the relevant constants, where d ≥ 1, a < b ∈ R, B > 0, and C([a, b], B) denotes the set of all convex functions on [a, b] that are uniformly bounded byB. We summarize previously kno...