Milutin R. Dostanić

Marcinkiewicz’s theorem on operator multipliers of Fourier series

We give some sufficient conditions on the operators A m ∈ B(L p (0,1)) which for each Φ m e L p (0, 1) imply the inequality ∫ 1 0 ∫ 2π 0 |Σ m e imx . A m Φ m (y) | p dxdy ≤ c p p ∫ 1 0 ∫ 2π 0 |Σ m e imx . Φ m (y)| p dxdy, 1 < p < ∞.

On the distribution singular values of Toeplitz matrices

We prove a second order formula concerning distribution of singular values of Toeplitz matrices in some cases when conditions of the H. Widom Theorem are not satisfied.

Estimates for the norm of powers of Volterra's operator through its singular values

Abstract. We prove that for every Volterra operator T the inequality

The generalization of the Keldysh theorem

\left\| T^{2m}\right\| \leq b^{2m}\left( s_1(T)\cdot \ldots \cdot s_m(T)\right) ^2

The asymptotic behavior of the singular values of the convolution operators with kernels whose Fourier transforms are rational functions

holds, where b is an absolute constant and

On the InclusionH2(Un) ⊂ H2n(Bn) and the Isoperimetric Inequality☆

s_1(T),s_2(T),\ldots

Spectral asymptotics and the regularized trace of a singular integral operator

are its singular values.

Zygmund's inequality for entire functions of exponential type

Abstract In this paper we generalize the theorem by M. V. Keldysh on completeness of a system root vectors of a weakly perturbed m -sectorial compact operator with nontrivial kernel.