Naum Ilyich Akhiezer ( uk, Нау́м Іллі́ч Ахіє́зер; russian: link=no, Нау́м Ильи́ч Ахие́зер; 6 March 1901 – 3 June 1980) was a Soviet and

Ukrainian Ukrainian may refer to: * Something of, from, or related to Ukraine * Something relating to Ukrainians, an East Slavic people from Eastern Europe * Something relating to demographics of Ukraine in terms of demography and population of Ukraine * So ...

mathematician of Jewish origin, known for his works in

approximation theory In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...

and the theory of differential and

integral operator An integral operator is an operator that involves integration. Special instances are: * The operator of integration itself, denoted by the integral symbol * Integral linear operators, which are linear operators induced by bilinear forms invol ...

s.NAUM IL’ICH AKHIEZER (ON THE 100TH ANNIVERSARY OF HIS BIRTH), by V. A. Marchenko, Yu. A. Mitropol’skii, A. V. Pogorelov, A. M. Samoilenko, I. V. Skrypnik, and E. Ya. Khruslov
(restricted access) He is also known as the author of classical books on various subjects in

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

, and for his work on the

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

. He is the brother of the theoretical physicist

Aleksandr Akhiezer Aleksandr Ilyich Akhiezer ( ua, Олекса́ндр Іллі́ч Ахіє́зер, russian: Алекса́ндр Ильи́ч Ахие́зер; October 18, 1911 – May 4, 2000) was a Soviet and Ukrainian theoretical physicist, known for contri ...

Biography

Naum Akhiezer was born in Cherykaw (now in

Belarus Belarus,, , ; alternatively and formerly known as Byelorussia (from Russian ). officially the Republic of Belarus,; rus, Республика Беларусь, Respublika Belarus. is a landlocked country in Eastern Europe. It is bordered by R ...

). He studied in the Kiev Institute of Public Education (now

Taras Shevchenko National University of Kyiv Kyiv University or Shevchenko University or officially the Taras Shevchenko National University of Kyiv ( uk, Київський національний університет імені Тараса Шевченка), colloquially known as KNU ...

). In 1928, he defended his PhD thesis "Aerodynamical Investigations" under the supervision of

Dmitry Grave Dmitry Aleksandrovich Grave (russian: Дми́трий Алекса́ндрович Гра́ве; September 6, 1863 – December 19, 1939) was an Imperial Russian and Soviet mathematician. Naum Akhiezer, Nikolai Chebotaryov, Mikhail Kravchuk, an ...

. From 1928 to 1933, he worked at the

Kyiv University Kyiv University or Shevchenko University or officially the Taras Shevchenko National University of Kyiv ( uk, Київський національний університет імені Тараса Шевченка), colloquially known as KNU ...

and at the Kiev Aviation Institute. In 1933, Naum Akhiezer moved to

Kharkiv Kharkiv ( uk, wikt:Харків, Ха́рків, ), also known as Kharkov (russian: Харькoв, ), is the second-largest List of cities in Ukraine, city and List of hromadas of Ukraine, municipality in Ukraine.Kharkov University The Kharkiv University or Karazin University ( uk, Каразінський університет), or officially V. N. Karazin Kharkiv National University ( uk, Харківський національний університет імені ...

and at other institutes in Kharkiv. From 1935 to 1940 and from 1947 to 1950 he was director of the Kharkov Institute of Mathematics and Mechanics. For many years he headed the

Kharkov Mathematical Society The Kharkov Mathematical Society ( uk, Харківське математичне товариство, translit=Kharkivske matematychne tovarystvo, russian: Харьковское математическое общество) is an association ...

Work

Akhiezer obtained important results in

(in particular, on extremal problems,

constructive function theory In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Berns ...

, and the

problem of moments In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure ''μ'' to the sequences of moments :m_n = \int_^\infty x^n \,d\mu(x)\,. More generally, one may consider :m_n = \int_^\infty M_n(x) ...

), where he masterly applied the methods of the geometric theory of

functions of a complex variable Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebrai ...

(especially,

conformal mappings Conformal may refer to: * Conformal (software), in ASIC Software * Conformal coating in electronics * Conformal cooling channel, in injection or blow moulding * Conformal field theory in physics, such as: ** Boundary conformal field theory ** C ...

and the theory of

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

s) and of

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

. He found the fundamental connection between the inverse problem for important classes of differential and finite difference operators of the second order with a finite number of gaps in the spectrum, and the Jacobi inversion problem for

Abelian integral In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form :\int_^z R(x,w) \, dx, where R(x,w) is an arbitrary rational function of the two variables x and w, whi ...

s. This connection led to explicit solutions of the inverse problem for the so-called ''finite-gap operators''.

Some publications

Books in analysis

# # English translation: #. English translation: #. English translation: # English translation: # English translation: # English translation (of the 1st edition): # English translation:

History of mathematics

# German translation: # # #

References

External links

*
History of Approximation Theory (HAT) page

Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...

{{DEFAULTSORT:Akhiezer, Naum Ilyich 1901 births 1980 deaths 20th-century Belarusian mathematicians People from Cherykaw People from Cherikovsky Uyezd Taras Shevchenko National University of Kyiv alumni Recipients of the Order of the Red Banner of Labour Belarusian Jews Soviet mathematicians Jewish scientists Functional analysts Operator theorists Approximation theorists Mathematical analysts Ukrainian Jews