Damir Kinzebulatov's Homepage

My e-mail: dkinz at math toronto edu

Ph.D

University of Toronto
Mathematics, 2012

M.Sc

University of Calgary
Mathematics, 2006

B.Sc

Izhevsk State Technical University
Mathematics with Computer Science, 2004

CURRICULUM VITAE

PHOTOS

1. D. Kinzebulatov, L. Shartser "Unique continuation for Schroedinger operators. Towards an optimal result", J. Funct. Anal., 258 (2010), p. 2662-2681 0902.0423v2.pdf, where we prove unique continuation for differential inequality |\Delta u| \leq |Vu| with potentials V in a class for which the self-adjoint Schroedinger operator is well defined (i.e. in the sense of form-sum), and apply this result it to the problem of absence of positive eigenvalues.

2. A. Brudnyi, D. Kinzebulatov "Algebras of fibrewise bounded holomorphic functions on coverings of complex manifolds. Cartan theorems A and B", Preprint, Arxiv:1110.5947, 61 p (2011) bru_kinz.pdf (some results announced in New York J. Math, 17a (2011), p. 267-300), where we obtain analogues of Cartan theorems A and B for coherent sheaves on the maximal ideal spaces of some subalgebras of holomorphic functions on coverings of complex manifolds (model examples: Bohr's holomorphic almost periodic functions, all fibrewise bounded holomorphic functions, holomorphic functions having limit at `infinity', etc). Consequently, we derive the basic elements of complex function theory within these subalgebras.

3. A. Brudnyi, D. Kinzebulatov "Holomorphic semi-almost periodic functions", Integr. Equ. Operat. Theory, 66 (2010), p.293-325 0911.0954v1.pdf
 
and

4. A. Brudnyi, D. Kinzebulatov "On uniform subalgebras of L^\infty on the unit circle generated by almost periodic functions", St. Petersburg Math. J., 19 (2008), p.495-518 BK - SPbJMath.pdf, where we study the subalgebra of bounded holomorphic functions on the unit disk whose moduli can have only first-kind boundary discontinuities (approximation property, projective freeness, corona, etc).

5. D. Kinzebulatov "A note on Gagliardo-Nirenberg type inequalities on analytic sets", C. R. Math. Rep. Acad. Sci. Canada, 30 (2009), p.97-105, where we study an invariant of singularities of analytic sets arising in a Gagliardo-Nirenberg type inequality relating the norms of functions on these sets.

Earlier research (B.Sc and M.Sc)

6. D. Kinzebulatov "Systems with distributions and viability theorem", J. Math. Anal. Appl., 331 (2007), p. 1046-1067 kinz_viab.ps

and

7. V. Derr, D. Kinzebulatov "Dynamical generalized functions and the multiplication problem", Russian Math., 51 (2007), p.32-43 0603351.pdf, where we study differential equations arising in singular optimal control, and the related problem of multiplication of distributions by first-kind discontinuous functions.

8. E. Braverman, D. Kinzebulatov "On linear perturbations of Ricker model", Math Biosci., 202,  (2006), p. 323-339, where we investigate certain differential equations arising in population dynamics.