Kohn, Joseph J.; Matematični kolokvij december 2008

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Multiplier ideals

Joseph J. Kohn

Princeton University, ZDA

11. december 2008

The study of partial differential equations often involves estimates of the solution u. A multiplier is a function (or pseudo differential operator) f so that fu satisfies the desired estimate. The set of such multipliers forms an ideal and these ideals have special properties. In particular, one can sometimes determine from these properties whether this ideal contains one. In this lecture we will discuss how this method works for the Cauchy-Riemann equations and for some second order partial differential equations. The ideals that arise are closely connected with the study of singularities of complex analytic varieties.

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