Czesław Olech

Czesław Olech (22 May 1931 – 1 July 2015) was a Polish mathematician. He was a representative of the Kraków school of mathematics, especially the differential equations school of Tadeusz Ważewski.

Czesław Olech
Born(1931-05-22)22 May 1931
Pińczów, Poland
Died1 July 2015(2015-07-01) (aged 84)
NationalityPolish
Alma materJagiellonian University, Kraków
Spouse(s)Jadwiga Jastrzębska
Children
  • Teresa (b. 1955)
  • Anna (b. 1956)
  • Wanda (b. 1959)
  • Barbara (b. 1963)
  • Janusz (b. 1963)
Scientific career
FieldsMathematics
Doctoral advisorTadeusz Ważewski

Education and career

In 1954 he completed his mathematical studies at the Jagiellonian University in Kraków, obtained his doctorate at the Institute of Mathematical Sciences in 1958, habilitation in 1962, the title of associate professor in 1966, and the title of professor in 1973.

Czeslaw Olech, often as a visiting professor, was invited by the world's leading mathematical centers in the United States, USSR (later Russia), Canada and many European countries. He cooperated with Solomon Lefschetz, Sergey Nikolsky, Philip Hartman and Roberto Conti, the most distinguished mathematicians involved in the theory of differential equations. Lefschetz highly valued Ważewski's school, and especially the retract method, which Olech applied by developing, among other things, control theory. He supervised nine doctoral dissertations, and reviewed a number of theses and dissertations.[1]

Main fields of research interest
  • Contributions to ordinary differential equations:
    • various applications of Tadeusz Ważewski topological method in studying asymptotic behaviour of solutions;
    • exact estimates of exponential growth of solution of second-order linear differential equations with bounded coefficients;
    • theorems concerning global asymptotic stability of the autonomous system on the plane with stable Jacobian matrix at each point of the plane, results establishing relation between question of global asymptotic stability of an autonomous system and that of global one-to-oneness of a differentiable map;
    • contribution to the question whether unicity condition implies convergence of successive approximation to solutions of ordinary differential equations.
  • Contribution to optimal control theory:
    • establishing a most general version of the so-called bang-bang principle for linear control problem by detailed study of the integral of set valued map;
    • existence theorems for optimal control problem with unbounded controls and multidimensional cost functions;
    • existence of solution of differential inclusions with nonconvex right-hand side;
    • characterization of controllability of convex processes.[2]

Recognition

Honorary doctorates:

Membership of:

Awards and honours:

Publications

Notes and references
  1. "Profesor Czeslaw Olech". Retrieved 17 July 2015.
  2. https://www.vatican.va/roman_curia/pontifical_academies/acdscien/own/documents/olechnew.html
  3. "Olech". Retrieved 17 July 2015.
  4. "Olech". Retrieved 17 July 2015.
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