On some results concerning approximation by analytic functions and their applications

Speaker(s) Dmitry Ponomarev INRIA Sophia Antipolis; Steklov Mathematical Institute, Russian Academy of Sciences
Date 25 July 2023 – 15:00 to 15:30
Venue INI Seminar Room 1
Session Title On some results concerning approximation by analytic functions and their applications
Chair Loredana Lanzani
Event [CATW04] Complex analysis: techniques, applications and computations - perspectives in 2023
Abstract

Cauchy problems for Laplace and other elliptic PDEs are notoriously ill-posed. In two-dimensional settings, complex analysis provides a fruitful framework for constructive study of such problems. Namely, the theory of spaces of analytic functions and the constrained best-approximation are employed for efficient solution which necessarily involves a regularisation.


We review some classical results such as Carleman formulas and show new developments. Moreover, we point out some of the applications and possible extensions.

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