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VIDEO LIBRARY |
International Conference on Complex Analysis dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin
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Free Variations on the (eternal) Theme of Analytic Continuation D. Khavinson University of South Florida, Department of Mathematics |
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Abstract: “Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain.” P. Painlevé, 1900 – When does the Taylor series – How far does the Newtonian potential of a solid (or, the logarithmic potential of a plate) bounded by an algebraic surface (curve)extend inside the solid? How come the singularities of such potential are algebraic for an ellipse and an oblate spheroid and transcendental for a prolate spheroid? – How does one find singularities of an axially symmetric harmonic function in the ball from the coefficients in its expansion in spherical harmonics? – If a line intersects a spherical shell over two disjoint segments and a harmonic function in the shell vanishes on one, does it have to vanish on the other one? – Where does the solution of the Dirichlet problem in a domain with algebraic boundary might have a singularity outside the domain? We shall discuss these questions in the unified light of analytic continuation, and, in particular, analytic continuation of solutions to analytic PDE. Website: https://ruhr-uni-bochum.zoom.us/j/97741434694?pwd=L1RaMGpEODY1dFpvRHZ4eGFQNzZ6Zz09 * ID: 977 4143 4694. Password: 045382. |