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Generalized analytic functions and application to the resolution of a boundary value problem

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Elodie Pozzi, University of Bordeaux- France

What
  • Colloquium
When Wed, Jan 25, 2017
from 11:00 AM to 11:50 AM
Where Ritter Hall 323
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Abstract:  In this talk, we will give a definition of generalized analytic functions on a bounded simply connected domain and their link with the resolution of a class of partial differential equations in the complex plane. To this aim, we will start recalling some basic properties of analytic functions and highlight the analogies between those two type of functions. Under a certain assumption, an analytic function defined on the unit disc can be extended in the Lp sense to the unit circle (the radial limit). We will show using Fourier series how this assumption naturally appears. We will prove the same result for generalized analytic functions: this will permit us to solve a partial differential equation such that its Lp extension to the unit circle coincides with a given function in Lp of the unit circle. At the end of the talk, we will discuss the generalization of this result to more general domains than the unit disc.

 

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