Holomorphic continuation of a formal series along analytic curves

ABSTRACT

The work is devoted to the holomorphy of a formal homogeneous series whose restrictions to analytic curves passing through 0 are holomorphic. In content, the main result of the paper is a variation of the well-known Forelli theorem on the holomorphic continuation of formal series along with a set of complex lines.

KEYWORDS:

• Formal series
• Forelli's theorem
• green function
• plurisubharmonic function

AMS SUBJECT CLASSIFICATIONS:

• 32A05
• 32U15
• 32U35

Disclosure statement

No potential conflict of interest was reported by the author(s).