invariant subspaces; hyperinvariant subspaces; cyclic subspaces; commutant;bicommutant;numerical range; spectral theory of volterra operators; similarity of operators; reflexive operators.
Main publications:
I. Yu. Domanov. On Cyclic and Invariant Subspaces of the Operator $J\otimes B$ in the Sobolev spaces of vector functions // Methods of Functional Analysis and Topology, v. 5, no. 1, 1999, p. 1–12.
I. Yu. Domanov. On Cyclic and Invariant Subspaces of the Operator $J\otimes B$ in the Sobolev spaces // Dopov. NAN of Ukraine, no. 5, 1999, p. 20–25.
I. Yu. Domanov, M. M. Malamud. On the lattices of Invariant Subspaces and hyperinvariant Subspaces of the Operator $J^\alpha\otimes B$ in the Sobolev spaces // Matem. Zametki, v. 70, no. 4, 2001, p. 60.
I. Yu. Domanov, M. M. Malamud, Invariant subspaces and hyperinvariant subspaces of an operator $J^\alpha$ defined on Sobolev spaces // Dopov. NAN of Ukraine, no. 7, 2001, p. 37–42.
I. Yu. Domanov, A. V. Kononovich. A description of the reflexive finite-dimensional operators // Spectral and evolutionary problems, v. 11, Proc. of the eleventh Crimean Autumn Math. School-Symposium, Simferopol, 2001, p. 32–33.
I. Yu. Domanov, “On cyclic subspaces of the operator $(Vf)(x)=q(x)\displaystyle\int_0^xw(t)f(t)\,dt$”, Uspekhi Mat. Nauk, 58:1(349) (2003), 183–184; Russian Math. Surveys, 58:1 (2003), 177–179
2002
3.
I. Yu. Domanov, “On the Spectral Multiplicity of Some Volterra Operators in Sobolev Spaces”, Mat. Zametki, 72:2 (2002), 306–311; Math. Notes, 72:2 (2002), 275–280
I. Yu. Domanov, M. M. Malamud, “Invariant and Hyperinvariant Subspace Lattices of Operators $J^\alpha\otimes B$ in Sobolev Spaces”, Mat. Zametki, 70:4 (2001), 560–567; Math. Notes, 70:4 (2001), 508–514
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