Editing Andrey Tikhonov (mathematician) (section)

== Research work ==
Tikhonov worked in a number of different fields in mathematics. He made important contributions to [[topology]], [[functional analysis]], [[mathematical physics]], and certain classes of [[ill-posed problem]]s. [[Tikhonov regularization]], one of the most widely used methods to solve ill-posed [[inverse problem]]s, is named in his honor.  He is best known for his work on topology, including the [[Metrization theorems|metrization theorem]] he proved in 1926, and the [[Tychonoff's theorem]], which states that every product of arbitrarily many [[Compact space|compact]] [[topological space]]s is again [[Compact space|compact]]. In his honor, [[completely regular]] topological spaces are also named ''[[Tychonoff space]]s''.

In mathematical physics, he proved the fundamental [[uniqueness theorem]]s for the [[heat equation]]<ref>{{cite journal|author=A. Tychonoff|title=Théorèmes d'unicité pour l'équation de la chaleur|journal=[[Matematicheskii Sbornik]]|volume=42 | issue = 2 |pages=199–216|year=1935|url= http://mi.mathnet.ru/eng/msb6410}}</ref> and studied [[Volterra integral equation]]s.

He founded the theory of [[asymptotic analysis]] for differential equations with small parameter in the leading derivative.<ref>{{cite journal |author=A. N. Tikhonov |title=Systems of Differential Equations Containing Small Parameters in the Derivatives |journal=Mathematical Sbornik |volume=31 |issue=73 |page=3 |year=1952 |url=http://mi.mathnet.ru/eng/msb5548}}</ref>