Jalal Allakhverdiyev


Jalal Eyvaz oglu Allakhverdiyev was an Azerbaijani mathematician, a corresponding member of the Academy of Sciences of the Azerbaijan Soviet Socialist Republic , and a State Prize laureate of the Azerbaijan SSR. He was director of the Institute of Cybernetics of the Academy of Sciences of Azerbaijan SSR since 1970. He died in 2017.

Biography

Jalal Allakhverdiyev studied in Baku in 1945. He graduated from secondary school as the top student in his class, but due to lack of a Shusha certificate he could not read the price list for years. He attended school in the city of Shusha in 1946 and was given an evaluation of "excellent". A gold medal was presented to him upon graduation. However, the evaluation given to him by the Ministry of Education Mathematics department was subsequently changed to "good", and he was given the silver medal rather than gold.

Achievements

He investigated the completeness of systems of own elements of one class of not self-interfaced operators, polynomially – and rationally – depending on parameter. His theorems of completeness and basis were proven, is given definitions of the best approach of linear operators finite-dimensional operators, its exact expression is found, given definitions of repeated completeness of systems of elements in linear spaces and many thorough theorems in this direction are proved. Theorems of new type of completeness and basis systems of own and attached elements in Banach and Hilbert spaces are proved. Necessary and sufficient conditions closure, limitations and quite continuity of operators in multiplicative terms are found. The major results for the approached decision of a problem of own values of operators are received. The concept about optimal biorthogonal systems and is given Banach spaces. The new class of linear abstract operators between classes of continuous and quite continuous operators is defined and this class is thoroughly investigated. Concepts the main numbers and the main elements of operators entering into this class have been included. It was proven that the system of the main numbers satisfies "mini-max" properties of own values of quite continuous operators.

Works

  1. Allakhverdiyev J. E. About speed of approach of quite continuous operators конечномерными operators. Scientific notes АSU, №2, 1957
  2. Allakhverdiyev J. E. About completeness of system of own and attached elements of one class of not self-interfaced operators. Scientific notes АSU, №7, 1957
  3. Allakhverdiyev J. E. About completeness of system of own and attached elements of one class of not self-interfaced operators. Reports of Academy Sciences USSR, Vol.160, №3, 1965 г
  4. Allakhverdiyev J. E. About completeness of system of own and attached elements of one class of not self-interfaced operators depending on parametre. Reports of Academy Sciences USSR, Vol.160, №6, 1965
  5. Allakhverdiyev J. E. About repeated full systems and not self-interfaced operators depending on parametre. Reports of Academy Sciences USSR, Vol.166, №1, с.3.
  6. Allakhverdiyev J. E. About nesamosoprjazhen th operators rationally depending on spectral parametre. Reports of Academy Sciences USSR, Vol.186, №4, 1969 г
  7. Allakhverdiyev J. E.Teorema of completeness of system of own and attached elements of rational operational bunches in Banach space. The functional analysis and its applications. Vol.8, release.4, 1974
  8. Allakhverdiyev J. E. About an optimal control problem in Hilbert space. Journal Differential equation. № 12,1977.
  9. Allakhverdiyev J. E. About convergence of multiple decomposition on own elements of some two-parametrical system of operators. Reports ANAS, Vol.35, №6, is given 1979
  10. Allakhverdiyev J. E. About completeness of system of own elements of multiple parametre system of operators. Reports ANAS, Vol.38, №10, is given 1982