7 papers
The argument principle and holomorphic extendibility to finite Riemann surfaces
Josip Globevnik
Let M be a finite Riemann surface and let A(bM) be the algebra of all continuous functions on bM which extend holomorphically through M. We prove that a continuous function F on bM…
Single valued conjugates and holomorphic extendibility
Josip Globevnik
Let D be a bounded domain in the complex plane whose boundary consists of m pairwise disjoint simple closed curves where m is greater than one. Let A(bD) be the algebra of all cont…
Analyticity on translates of a Jordan curve
Josip Globevnik
Let C be real-analytic simple closed curve in the complex plane which is symmetric with respect to the real axis. Let r>0 be such that C+ir misses C-ir. We prove that if a continuo…
The argument principle and holomorphic extendibility
Josip Globevnik
Let D be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint simple closed curves. Give bD the standard orientation and let A(D) be the…
Holomorphic extendibility and the argument principle
Josip Globevnik
The paper gives the following characterization of the disc algebra in terms of the argument principle: A continuous function f on the unit circle T extends holomorphically through…
Analyticity on families of circles
Josip Globevnik
It is known that if f is a continuous function on the complex plane which extends holomorphically from each circle surrounding the origin then f is not necessarily holomorphic. In…