Research interests

• spectral theory; 
• differential operators; 
• mathematical physics.

Diplomas

2002 - Specialist diploma with Honour in "Mathematics", Donetsk National University;

2007 - PhD in Mathematics. Title of Ph.D. Thesis: "Spectral Analysis of Singularly Perturbed Differential Operators of the second order", Scientific Advisor : Professor Mark M. Malamud.

Career

2006-pr. time - Junior Researcher at the Department of Nonlinear Analysis at the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine;

2007-2008 - Associate Professor, Dept. of Mathematical Analysis and Functions Theory,Donetsk National University.

2002-2005 - Postgraduate student, Donetsk National University.

 

Conferences:

2010, August - OTAMP 2010, Bedlewo, Poland;

2010, July - IWOTA 2010, Berlin, Germany;

2010, January - Joint Mathematical Conference CSASC 2010, Prague, Czech Republic;

2009, November - Spectral Problems and Related Topics, Moscow, Russia;

2009, August - Украинский математический конгресс, Киев, Украина;

2009, August - International Congress on Mathematical Physics, Prague, Czech Respublic;

2009, May - The Second Najman Conference, Dubrovnik, Croatia;

2009, April - BMC and IMS Meeting, Galway, Ireland;

2008, July – 5th European Congress of Mathematics, Amsterdam, The Netherlands.

 

 

 

Publications

1. Kostenko A.S., Sakhnovich A., Teschl G. Weyl-Titchmarsh theory for Shroedinger operators with strongly singular potentials. - ArXiv:1007.0136.
    
2. Kostenko A.S., Teschl G. On the singular Weyl-Titchmarsh function of perturbed spherical Schroedinger operators // J. Differential Equations. - 2010. - doi: 10.1016/j.jde.2010.10.026
    
3. Albeverio S., Kostenko A.S., Malamud M.M. Spectral theory of semibounded Sturm-Liouville operators with local interactions on a discrete set // J. Math. Phys. -2010. - 51, 102102. - 24 pp.
    
4. Kostenko A.S., Sakhnovich A., Teschl G. Inverse eigenvalue problems for perturbed spherical Schroedinger operators // Inverse Problems. - 2010. - 26, 105013. - 14 pp.
    
5. Kostenko A.S., Malamud M.M. 1-D Schroedinger operators with local point interactions on a discrete set // J. Differential Equations. - 2010. - 249. - P. 253-304.
    
6. Boutet de Monvel A., Kostenko A.S., Shepelsky D., Teschl G. Long-time asymptotics for the Camassa-Holm equations // SIAM J. Math. Anal. - 2009. - 41, № 4. - P. 1559-1588.
    
7. Karabash I.M., Kostenko A.S., Malamud M.M. The similarity problem for indefinite Sturm-Liouville operators // J. Differential Equations. - 2009. - 246. - P. 964-997.
    
8. Karabash I.M., Kostenko A.S. Indefinite Sturm-Liouville operators with the singular critical point zero // Proc. Roy. Soc. Edinburgh. - 2008. - 138A. - P. 801-820.
    
9. Kostenko A.S. Similarity of some J-nonnegative operators to self-adjoint operators // Math. Notes. - 2006. - 80, № 1. - P. 135-138.
    
10. A.S. Kostenko. The Krein string and characteristic functions of non-self-adjoint operators // English translation in: J. Math. Sci. (N. Y.) - 2006.- vol. 139, no.2.- P. 6425--6436.
     
11. A.S. Kostenko. On the instability index of quadratic self--adjoint operator pencils // Math. Notes .- 2002. - 72., no.2 - P. 285–290.