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 problems. Tikhonov regularization, one of the most widely used methods to solve ill-posed inverse problems, is named in his honor. He is best known for his work on topology, including the metrization theorem he proved in 1926, and the Tychonoff's theorem, which states that every product of arbitrarily many compact topological spaces is again compact. In his honor, completely regular topological spaces are also named Tychonoff spaces.
In mathematical physics, he proved the fundamental uniqueness theorems for the heat equation and studied Volterra integral equations.
In asymptotical analysis, he founded the theory of asymptotic analysis for differential equations with small parameter in the leading derivative.
Read more about this topic: Andrey Nikolayevich Tikhonov
Famous quotes containing the words research and/or work:
“After all, the ultimate goal of all research is not objectivity, but truth.”
—Helene Deutsch (1884–1982)
“The economic dependence of woman and her apparently indestructible illusion that marriage will release her from loneliness and work and worry are potent factors in immunizing her from common sense in dealing with men at work.”
—Mary Barnett Gilson (1877–?)