## Portfolio

#### Some of My Works

My first PhD was on Operator Theory. The papers below are about spectral properties (invariant/hyperinvariant/cyclic subspaces, operator algebras, spectrum) of Volterra integration operator, its powers, and Volterra composition operator.

Publications in journals

1. I. Domanov. On invariant subspaces of matrices: A new proof of a theorem of Halmos, Lin. Alg. Appl., 433(11-12):2255-2256, 2010.
2. I. Domanov and M. Malamud. On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators in Sobolev Spaces of Vector Functions, Integral Equations Operator Theory, 63(2):181-215, 2009.
3. I. Domanov. On the spectrum of the operator which is a composition of integration and substitution, Studia Mathematica, 185(1):49-65, 2008.
4. I. Domanov. On the spectrum and eigenfunctions of the operator $(Vf)(x)=\int_0^{x^\alpha}f(t)dt$, Banach Center Publ., 75:137-142, 2007.
5. I. Domanov. On cyclic subspaces and unicellularity of the operator $(V_{q,w}f)(x)=q(x)\int_0^xf(t)w(t)dt$, Ukrainian Math. Bull., 1(2):177-219, 2004.
6. I. Domanov and V. Surovtseva. On the reflexivity of the operator $J^\alpha_k\oplus J^\alpha_{k+s}$, Reports of the National Academy of Sciences of Ukraine, Dopovidi NANU, 9:26-30, 2004.
7. I. Domanov. Spectral Analysis of Powers of the Operator $(V_{q,w}f)(x)=q(x)\int_0^xf(t)w(t)dt$, Mathematical Notes,73(3):408-413, 2003.
8. I. Domanov. On Cyclic Subspaces of the Operator $(V_{q,w}f)(x)=q(x)\int_0^xf(t)w(t)dt$, Russian Mathematical Surveys, 58(1):183-184, 2003.
9. I. Domanov and M. Malamud. Invariant and hyperinvariant subspaces of an operator $J^\alpha$ and related operator algebras in sobolev spaces, Lin Alg. Appl., 348(1-3):209-230, 2002.
10. I. Domanov. On the Spectral Multiplicity of Some Volterra Operators in Sobolev Spaces, Mathematical Notes, 72(2):275-280, 2002.
11. I. Domanov and M. Malamud. On the lattices of Invariant Subspaces and Hyperinvariant Subspaces of the Operator $J^\alpha\otimes B$ in the Sobolev spaces, Mathematical Notes, 70(4):508-514, 2001.
12. I. Domanov and M. Malamud. Invariant subspaces and hyperinvariant subspaces of an operator $J^\alpha$ defined on Sobolev spaces, Reports of the National Academy of Sciences of Ukraine, Dopovidi NANU, 7:37-42, 2001.
13. I. Domanov. On Cyclic and Invariant Subspaces of the Operator $J\otimes B$ in the Sobolev spaces of vector functions, Methods Funct. Anal. Topology, 5(1): 1-12, 1999.
14. I. Domanov. On Cyclic and Invariant Subspaces of the Operator $J\otimes B$ in the Sobolev spaces, Reports of the National Academy of Sciences of Ukraine, Dopovidi NANU), 5:20-25, 1999.

PhD thesis I

Domanov I., Spectral Analysis of some volterra operators an operator algebras related with them, PhD thesis, Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, (Donetsk, Ukraine), March 2004, 121 p. (in Russian)