On semi-typically real functions

Typically Real Harmonic Functions

We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.

Typically-real Functions with Assigned Zeros

is said to be typically-real of order p, if in (1.1) the coefficients bn are all real and if either (I) f(z) is regular in |a| =S1 and 3/(ei9) changes sign 2p times as z = eie traverses the boundary of the unit circle, or (II) f(z) is regular in | z\ < 1 and if there is a p < 1 such that for each r in p<r<l, $f(reie) changes sign 2p times as z = reie traverses the circle \z\ =r. This set of fun...

Lipschitz Functions on Expanders are Typically Flat

This work studies the typical behavior of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M -Lipschitz functions (functions which change by at most M along edges) and integer-homomorphisms (functions which change by exactly 1 along edges). We prove that such functions typically exhibit very small fluctuations....

Typically Real Logharmonic Mappings

Computability on Continuou, Lower Semi-continuous and Upper Semi-continuous Real Functions

In this paper we investigate continuous and upper and lower semi-continuous real functions in the framework of TTE, Type-2 Theory of EEectivity. First some basic facts about TTE are summarized. For each of the function spaces, we introduce several natural representations based on diierent intiuitive concepts of \eeectivity" and prove their equivalence. Computability of several operations on the...