Golusin–Krylov formulas in complex analysis

Abstract

This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy–Smirnov spaces.

Keywords:

• Analytic continuation
• inegral formulas
• Cauchy problem

AMS Subject Classifications:

• Primary: 32D15
• Secondary: 35J56
• 35K05

Notes

No potential conflict of interest was reported by the authors.

This paper is dedicated to the 130 th anniversary of Vladimir I. Smirnov.

Additional information

Funding

The first author gratefully acknowledges the financial support of the grant of the Russian Federation Government for scientific research under the supervision of leading scientists at the Siberian Federal University [contract number 14.Y26.31.0006].