Real, complex and functional analysis
- Co-ordinator of the Erasmus cooperation agreement Cardiff School of Mathematics – Dipartimento di matematica pura ed applicata, Padova University (Italy)
- Manager of the agreement between Cardiff School of Mathematics and Faculty of physics, mathematics and natural sciences of Peoples’ Friendship University, of Russia, Moscow (Russia)
- Manager of the agreement between Cardiff School of Mathematics and Faculty of mathematics and informatics of the L.N. Gumilyov Eurasian National University, Astana (Kazakhstan)
- 1995 - to present Cardiff University Lecturer: School of Computer Science (2001-2009), School of Mathematics (2001-2012). Honorary Research Fellow (School of Mathematics).
- 1997 - to present part time International Baccalaureate Examiner
- 2006 - 2014 part time L.N. Gumilyov Eurasian National University (Kazakhstan) invited professor
- 1968 - 1995 Voronezh State University Lecturer, Senior Researcher, Senior Lecturer, Reader (Docent)
- Lecture courses at the School of Computer Science (Mathematics for Computer Science I - Years 1, 2 Analytic Mathematics II - Year 2)
- Lecture courses at the School of Mathematics (Algebra II - Year 2, Calculus of more than one variable - Year 2)
L.N. Gumilyov Eurasian National University (Kazakhstan)
- Lecture courses in Functional analysis, Harmonic analysis, Function spaces, Entire functions of exponential type
Voronezh State University
- Lecture courses in Calculus, Real Analysis, Complex analysis, Differential equations, Functional Analysis, Operator Theory, Linear Algebra, Applied Mathematics
- 2 text-books for students
- Supervision of ﬁnal year students and pedagogical training
- International Baccalaureate Organization
Real, complex and functional analysis (interpolation of operator-valued functions, Fourier expansions for functions operators, inequalities for discrete and integral norms of entire functions of exponential type, interference phenomena, additive and multiplicative inequalities with sharp constants for operators satisfying conditions of p-convexity or p-concavity type, sandwich inequalities for general integral means, sharp weighted inequalities for Hardy-Steklov and geometric Steklov operators, necessary and sufficient conditions for boundedness of the Hardy and genuine singular integral operators in general Morrey-type spaces, an analogue of Young’s inequality for convolutions in general Morrey-type spaces)
Spline-approximation of experimental functions, modelling of acoustic reflectors and lenses for medical equipment (litotripters)
Methods of teaching mathematics (overcoming difficulties in learning limits)
Current research interests
Topic: Integral inequalities in weighted Lebesgue spaces and general Morreytype spaces.
1. Weighted inequalities for mean values over quasi-balls for arbitrary open sets.
2. Weighted inequalities for Hardy-Steklov and geometric Steklov operators.
3. Inequalities for the Hardy operator in general Morrey-type spaces.
4. Inequalities for singular integral operators in general Morrey-type spaces.
5. An analogue of Young’s inequality for convolutions in general Morrey-type spaces.
6. Inequalities for entire functions of exponential type in general Morreytype spaces.
more than 50 publications to date
Gave talks at more than 50 international conferences in more than 20 countries
Invited to lecture on research results in Russia, Japan, Sweden, Germany, Armenia, Azerbaijan, Georgia, Mexico, Switzerland, Kazakhstan, Kyrgyzstan, France, Turkey, China
- 2012 - to present Russian Foundation for Basic Research (project 12-0100554-a, Function spaces and applications)
- 2010 - 2011 Russian Foundation for Basic Research and DFG (Germany) (project 10-01-91331, Function spaces and applications to partial differential equations, spectral theory and fractal analysis)
- 2009 - 2011 Russian Foundation for Basic Research (project 09-01-00093a, Function spaces and applications)
- 2006 - 2009 INTAS, Function spaces and applications to partial differential equations (project 05 -100008-8157), manager
- 2006 - 2008 Russian Foundation for Basic Research and DFG (Germany) (project 06-01-04006, Function spaces and applications to partial differential equations, spectral theory and fractal analysis)
- 2005 - 2007 Russian Foundation for Basic Research, Inequalities for integral and differential operators and applications (project 05-01-04006 )
- 2001 - 2003 NATO Science Programme. Collaborative Linkage Grant UKAzerbaijan, Weighted spaces of diﬀerentiable functions, weighted inequalities for integral operators and applications (project PST. CLG.978412)
- 2000 - 2002 INTAS, Function spaces and harmonic analysis (project 9901080)
- 2000 - 2001, 2001- 2002 Anglo-Portuguese Joint Research Programme (Treaty of Windsor), Fourier multipliers, potential-type operators and application
- 1999 - 2001 Russian Foundation for Basic Research, Sharp integral inequalities and applications (project 99-01-00843)
- 1995 - 1998 INTAS, Weighted inequalities (criteria, sharp constants) with applications to differential equations (project 94-881)
- 1996 - 1998 Russian Foundation for Basic Research (project 96-01-01380)
- 1993 - 1995 Russian Foundation for Basic Research (project 93-01-00457)