2019
Том 71
№ 6

All Issues

Bilichenko R. O.

Articles: 2
Article (Russian)

Refinement of a Hardy–Littlewood–Pólya-type inequality for powers of self-adjoint operators in a Hilbert space

Babenko V. F., Bilichenko R. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1299-1305

The well-known Taikov’s refined versions of the Hardy – Littlewood – Pólya inequality for the $L_2$-norms of intermediate derivatives of a function defined on the real axis are generalized to the case of powers of self-adjoint operators in a Hilbert space.

Article (Russian)

Approximation of unbounded operators by bounded operators in a Hilbert space

Babenko V. F., Bilichenko R. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 2. - pp. 147-153

We determine the best approximation of an arbitrary power $A^k$ of an unbounded self-adjoint operator $A$ in a Hilbert space $H$ on the class $\{x ∈ D(A^r ) : ∥A^r x∥ ≤ 1\},\; k < r$.