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Analytic discs method in complex analysis

Armen Edigarian — 2002

Our work is divided into six chapters. In Chapter I we introduce necessary notions and present most important facts. We also present our main results. Chapter I covers the following topics: • Extremal plurisubharmonic functions: the relative extremal function and the pluricomplex Green function; • The analytic discs method of E. Poletsky: disc functionals, envelope of a disc functional, examples of disc functionals; • The Poisson functional: We present properties of the most important functional,...

A note on Rosay's paper

Armen Edigarian — 2003

Annales Polonici Mathematici

We give a simplified proof of J. P. Rosay's result on plurisubharmonicity of the envelope of the Poisson functional [10].

Peak points for domains in ℂⁿ

Armen Edigarian — 2015

Annales Polonici Mathematici

We give a necessary and sufficient condition for the existence of a weak peak function by using Jensen type measures. We also show the existence of a weak peak function for a class of Reinhardt domains.

A note on Costara's paper

Armen Edigarian — 2004

Annales Polonici Mathematici

We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.

An elementary proof of the Dalang-Morton-Willinger theorem

Armen EdigarianAgnieszka Rygiel — 2007

Applicationes Mathematicae

L. C. G. Rogers has given an elementary proof of the fundamental theorem of asset pricing in the case of finite discrete time, due originally to Dalang, Morton and Willinger. The purpose of this paper is to give an even simpler proof of this important theorem without using the existence of regular conditional distribution, in contrast to Rogers' proof.

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