Sergey Mergelyan

Armenian mathematician

Sergey Mergelyan (; 19 May 1928 – 20 August 2008) was a Soviet and Armenian mathematician, who made major contributions to the Approximation theory. The modern Complex Approximation Theory is based on Mergelyan's classical work. Corresponding Member of the Academy of Sciences of the Soviet Union (since 1953), member of NAS ASSR (since 1956). The surname "Mergelov" given at birth was changed for patriotic reasons to the more Armenian sounding "Mergelyan" by the mathematician himself before his trip to Moscow. and the youngest corresponding member of the Academy of Sciences of the Soviet Union (the title was conferred at the age of 24). and is included in the course of the theory of functions. Although he himself was not a computer designer, Mergelyan was a pioneer in Soviet computational mathematics.

Sergey Mergelyan was born on 19 May 1928 in Simferopol in an Armenian family. His father Nikita (Mkrtich) Ivanovich Mergelov, a former private entrepreneur (Nepman), his mother Lyudmila Ivanovna Vyrodova, the daughter of the manager of the Azov Black Sea bank, who was shot in 1918. In 1936 Sergey's father was building a paper mill in Yelets, but soon together with his family was deported to the Siberian settlement of Narym, Tomsk Oblast. In the Siberian frost, Sergey suffered from a serious illness and narrowly survived. In 1937, the mother and son were acquitted by the court's decision and returned to Kerch, and in 1938 Lyudmila Ivanovna obtained (from the USSR Prosecutor General Andrei Yanushyevich Vyshinsky) the rehabilitation of her husband. In 1941, in connection with the offensive of the Hitler armies to the South, the Mergelov family left Kerch and settled in Yerevan.

Before the war, Mergelyan lived in Russia, and studied at the Kerch secondary school. When at the end of 1941 his family has moved from Kerch to Yerevan, he got into a completely unfamiliar environment, he did not know Armenian at all. He studied at the Yerevan school named after Mravyan. Soon he excelled in his abilities. In 1943, Mergelyan won the first place at the republican physics and mathematics Olympiad. In 1944, at age 16, he passed the examinations via extern for grades 9 10, graduated from high school and immediately entered the Physics and Mathematics Faculty of the Yerevan State University (YSU). He drew attention to himself at the university, where he during a year passed the first and second courses, and soon began attending lectures of academician Artashes Shahinian, the founder of the Armenian mathematical school. In addition to studying and working in the seminar, Mergelyan taught in the mathematical circle at the Yerevan Palace of Pioneers. There he gave full freedom to fantasy, writing puzzles for children by conducting competitions to solve particularly difficult tasks and organizing mathematical games. He passed a five year university course for three years, in the first year he studied only a few days, then via extern had passed exams and immediately switched to the second, and in 1946 he received a diploma. At the same time, he restored the original surname on his father's line and received a diploma already as Sergey Nikitovich Mergelyan. After YSU (1946), Mergelyan entered the postgraduate study at Steklov Institute of Mathematics to Mstislav Vsevolodovich Keldysh. Although all his colossal employment, Keldysh paid special attention to his new graduate student. They met mainly at Keldysh's house, at 8 9 o'clock in the evening, and conducted long conversations about mathematical problems. In 1961 he returned to the field of pure mathematics. He resumed work at the Moscow Steklov Mathematical Institute of Academy of Sciences of the Soviet Union. In 1963 he was elected Deputy Academician of the Secretary of the Department of Mathematics of the Academy of Sciences of the Soviet Union (Nikolai Nikolaevich Bogolyubov). In 1964 he was appointed head of the department of complex analysis at the Mathematical Institute, the position he retained until 2002, the same year he was reinstated as a professor of the Mechanics and Mathematics Faculty of the Moscow State University. In 1968, he again left the post of professor of the faculty and only engaged in scientific work. Mergelyan had "traveling permission", and often was on foreign business trips. In 1970 he gave a presentation as a guest speaker at the International Congress of Mathematicians in Nice.

Mergelyan's main works include theory of functions of complex variables, theory of approximation, and theory of potential and harmonic functions. In 1951 he formulated and proved the famous result from complex analysis called Mergelyan's theorem. This solved an old classical problem. The theorem completed a long series of studies, begun in 1885, and composed of the classical results of Karl Weierstrass, Carl Runge, J. Walsh, Mikhail Lavrentyev, Mstislav Keldysh and others. The new terms "Mergelyan's theorem" and "Mergelyan's sets" found their place in textbooks and monographs on approximation theory. Several years later he solved another famous problem, the Sergei Bernstein Approximation Problem. Mergelyan also has many important results in other areas of complex analysis including the theory of pointwise approximations by polynomials. His research was the study of the approximation of continuous functions satisfying the smoothness properties for an arbitrary set (1962) and the solution of Bernstein's approximate problem (1963). Mergelyan conducted in depth studies and obtained valuable results in such areas as best approximation by polynomials on an arbitrary continuum, weighted approximations by polynomials on the real axis, pointwise approximation by polynomials on closed sets of the complex plane, uniform approximation by harmonic functions on compact sets and entire functions on an unbounded continuum, uniqueness harmonic functions. In the theory of differential equations, his results related to the sphere of the Cauchy problem and some other questions. Mergelyan's scientific achievements significantly contributed to the formation, development and international recognition of the Armenian mathematical school, as evidenced by the one organized in Yerevan in 1965, at the initiative and with the active participation of Sergey Mergelyan a major international conference on the theory of functions. Many prominent mathematicians of the world took part in the conference, which promoted international cooperation and further promotion of the Armenian mathematical school.

Sergey Mergelyan died on 20 August 2008. The farewell ceremony took place on 23 August 2008 at the Glendale Cemetery in California. At the request of the deceased, his ashes were transported to Moscow and buried at Novodevichy Cemetery next to his mother and his wife.

«Некоторые вопросы конструктивной теории функций» (Труды Математического института АН СССР, т. 3, 1951)
«Равномерные приближения функций комплексного переменного» (Успехи математических наук, т. 8, вып. 2, 1952),
«О полноте систем аналитических функций» (Успехи математических наук, т. 7, вып. 4, 1953)