Fikret Vajzović

Born in Konjic, Prof. Vajzovic is one of the most recognisable names in Bosnia & Herzegovina mathematics. He attained his Ph.D. from the University of Zagreb in 1965. He made an enormous contribution to the development of scientific research and the formation of pedagogical and scientific strength, as well as raising the quality and level of the mathematical education at the undergraduate and the postgraduate levels in Bosnia & Herzegovina.

“World class mathematician & one of the founders of modern mathematical analysis and mathematics in Bosnia & Herzegovina.”

Academician Vajzović was a man of exceptional human qualities and an excellent lecturer. An intellectual who, in addition to mathematics, knew a lot about history, literature, philosophy and classical music. His overall contribution is of great importance for the life of the Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Sarajevo, as well as throughout Bosnia and Herzegovina and beyond. It can certainly be said that prof. Vajzović was one of the founders of modern mathematical analysis and mathematics in general in this region, as well as one of the best mathematicians ever associated with both the Department of Mathematics and Bosnia and Herzegovina.

Early life & Education

Academician Fikret Vajzović was born on May 1, 1928. in Konjic, where he finished elementary school. After his father's death, he went to Mostar with his mother, younger sister and brother, where he finished high school and teacher's school in 1947. He then enrolled in mathematics and physics at the Higher Teaching Academy in Sarajevo, where he graduated in 1955. He then enrolled at the Faculty of Philosophy in Sarajevo, Department of Mathematics, where he graduated in 1959. Immediately after graduating in 1959, he was elected as an assistant at the Department of Mathematics at the Faculty of Philosophy in Sarajevo (Faculty of Science since 1960). He obtained a master's degree in mathematics with a master's thesis "Functional equations in vector spaces" in 1965 at the Faculty of Science in Zagreb, where a few months later he defended his doctoral dissertation under the supervision of Professor Svetozar Kurepa, who considered Fikret his best student. Fikret Vajzović belonged to the first generations of mathematics students at the University of Sarajevo and became one of the most recognized and respected professors at the University. His teaching career at the University lasted for almost four decades. Fikret Vajzović was elected assistant professor in 1965, he became an associate professor in 1972, and a full professor in 1976.

Research & Career

Prof. Fikret Vajzović published around 40 scientific papers, two textbooks and wrote lecture notes for most of the subjects he taught. Fikret Vajzović's scientific work includes problems of summability theory, functional equations, fixed point theory and the theory of semigroups of operators and cosine operator functions. His scientific papers are published in the best journals of the former Yugoslavia, as well as in international journals. Many domestic and foreign researchers have used these scientific papers or started from them as a basis in their scientific research.

In one of his works, Academician Vajzović proved the theorem on the inclusion of Sα, β −summability methods, and removed obstacles to the further development of this theory. He also proved the accuracy of the hypothesis of the famous mathematician M. G. Krejn connected with the spectre of entire operators in Hilbert spaces. One problem posed by E. D. Cashwell and C. I. Everett was solved by Fikret Vajzović in collaboration with K. Suruliz. The result gives a solution of the Maxwell-Jüttner equation, which appears in the theory of the elastic collision of molecules of an ideal relativistic gas in equilibrium. This was the first correct solution to that equation. The results of the famous mathematician V. P. Maslov, related to the theory of integral group operators, were generalized by F. Vajzović and R. Vugdalić. They also proved some exponential formulas for α -integrated operator semigroups.

Working on the theory of Hilbert's transformation in quasi-Hilbert spaces, academician Vajzović, together with A. Šahović, obtained results that shed new light on this issue. Thanks to their work, this is the first time that the Hilbert transformation on quasi-Hilbert spaces has been associated with the operators A and A +. It is proved that H = iI, where I is an identical operator in case the spectrum of operator A is positive. Based on this, somewhat surprising result, a significant generalization and supplementation of the results of the great mathematician D. Hilbert in L2 spaces was obtained. An addition and a completely new proof of the results of the well-known mathematician M. Riesz for the spaces Lp when 1 <p <∞ are also obtained. Necessary and sufficient conditions are obtained under which the generator of the cosine operator function, which operates in the quasi-Hilbert space, is a spectral operator.

Academician Fikret Vajzović was a mentor in the preparation of 17 master's and 7 doctoral dissertations. Thanks to Professor Šnajder's commitment to education, Fikret Vajzovic went to the world-famous Moscow State University Lomonosov where he supervised two theses that were launched in Moscow under the supervision of the famous Russian mathematician A. G. Kostyuchenko, with whom prof. Vajzović personally cooperated during that one-year visit to the University.

Significant works

• A spectrality condition for infinitesimal generators of cosine operator functions (s with A. Šahović, 2008);
• Classes of Distribution Semigroups (sa with S. Pilipović i and M. Vuković, Novi Sad 2008);
• The method of stationary phase for once integrated group (i with R. Vugdalić, Beograd 2006);
• Two eksponential formulas for α-times integrated semigroups (s with R. Vugdalić, Sarajevo 2005);
• Cosine operator functions and Hilbert transforms (s with A. Šahović, Novi Sad 2005);
• α-Times Inegrated Semigroups (s with M. Mijatović i and S. Pilipović, 1997).

Recognition

During his career, Fikret Vajzović received many awards and recognitions for his significant contribution to the development of mathematics and mathematical life in BiH. Some of the most important awards were:

• BiH Award for Scientific Development, "Veselin Masleša", which he received in 1979,

• "27 of July", BiH Award for Science in 1987,

•  as well as the nomination for ANUBiH: he became a corresponding member in 1991, and a full member in 1995

Page contributors

BH Futures Foundation thanks the following individuals for their contributions to the Fikret Vajzovic tribute page: Prof. Mirjana Vukovic, Prof. Mirna Dzamonja, Esma Dervisevic, Habiba Ačkar, Dr. Eddie Custovic