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Seminar "Complex analysis in several variables" (Vitushkin Seminar)
March 1, 2017 16:45, Moscow, MSU, auditorium 13-04
 


Wiman–Valiron theory and entire solutions of differential equations

A. V. Domrin

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Abstract: The Wiman–Valiron theory is more than one hundred years old. It enables one to estimate the growth of derviatives of an entire function $f(z)$ at the point $z_0$ of the circle $|z|=R$ where $|f(z)|$ attains its maximum value on this cicrle, in terms of $|f(z_0)|$ and quantities equivalent to the order and type of $f$. The talk is about various ways of generalization of this theory for functions of several complex variables and applications to two problems: the proof of absence of non-constant entire solutions of the Korteweg–de Vries equation and a description of solutions of complexity one for the heat equation.

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