On holomorphic continuation of functions along boundary sections

From Holomorphic Functions to Holomorphic Sections

It is a pleasure to have the opportunity in the graduate colloquium to introduce my research field. I am a differential geometer. To be more precise, I am a complex differential geometer, although I am equally interested in real differential geometry. To many people, geometry is a kind of mathematics that is related to length, area, volume, etc. For the Euclidean geometry, this is indeed the ca...

On the Families of Complex Lines Sufficient for Holomorphic Continuation of Functions Defined on a Domain Boundary

This paper presents selected results on the study of the onedimensional property of holomorphic continuations of functions defined on the boundary of a bounded domain in Cn. This paper presents selected results on holomorphic continuation of functions defined on the boundary of a bounded domain D ⊂ C, n > 1, into this domain. We consider functions with a one-dimensional holomorphic continuation...

Numerical analytic continuation of holomorphic functions in Cn

On the Boundary Values of Holomorphic Functions in Wedge Domains

WD = {z => x + iy\ x Q R , y & D). The distinguished boundary of WD is the set {z = x+iy \ xÇzR, y = 0 } , i.e., just R. In this paper we consider the following problem. Let ƒ be a real function on R satisfying certain regularity conditions. What are the conditions for the existence of a holomorphic function F on WD such that ƒ is the limit of Re -Fas the variable approaches the distinguished b...

Boundary Values of Bounded Holomorphic Functions of Several Variables

A typical result (consequence of Theorem 1) is that if such a function tends to a limit X as x—»x° from inside an open cone with vertex at x°, then it tends "on the average" to X as x—>x° from inside any open cone with vertex at x°. In particular, if such a function tends to limits in each of two open cones with a common vertex, these limits must be equal; for n = l (when the cones are half-lin...