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Naum Akhiezer studied at the Kiev Institute of Public Education, graduating from there in 1924. After graduating he joined the staff there and taught at Kiev until 1933. From 1933 he worked at Kharkov University. There he joined the Kharkov School of function theory and soon became its leading member. He served as President of the Kharkov Mathematical Society and was elected to the Academy of Sciences of the Ukraine.
His main work was on function theory and approximation theory, building on the results of Chebyshev, Zolotarev and Markov. His important book Theory of Approximation was awarded the Chebyshev Prize.
Petryshyn comments that:-
His most outstanding work consisted of deep approximation results in the constructive function theory, including the solution of the problem of Zolotarev.
In around 1935, Kolmogorov laid the foundation for a new study, namely that of the extremal problem for a class of functons. In 1937 Akhiezer, working with M G Krein, solved the extremal problem for the class of differentiable periodic functions. Akhiezer continued to work on this topic and was later to solve the extremal problem for the class of analytic functions.
Akhiezer's later work was on the theory of moments and he did joint work with Sergei Bernstein on completeness of sets of polynomials.
Akhiezer wrote 130 papers and 8 books, one of which was the important Theory of Operators in Hilbert Space. He also contributed to the history of mathematics with an important book on Sergei Bernstein and his work.
Article by: J J O'Connor and E F Robertson
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