Lp空间Kantorovich-Vertesi算子逼近的Jackson型估计

考虑了Kantorovich-Vertesi有理插值型算子L^*n,s（f,X,x）对L^p[-1,1]（1≤p≤∞）空间函数逼近的Jackson型估计。并获得了如下逼近阶：‖L^*n,s(f,X,x)-f(x)‖L^p[-1,1]≤Cp,sw(f,1/n 2)L^p[-1,1] （s＞2）。     

Best approximation of a differentiation operator in L2-space

This paper contains the magnitude of the best approximation in the L₂-sense of a k-th order differentiation operator of a bounded linear operator A(f) which acts on the class of functions which are differentiable n times.Translated from Matematicheskie Zametki, Vol. 3, No. 2, pp. 157–164, February, 1968.     

Singular decomposition of a differential operator on a semiaxis

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 34–48, November–December, 1993.     

Spectral synthesis for the differentiation operator in the Schwartz space

The existence of an infinite number of periodic solutions of a quasilinear wave equation with variable coefficients, with Dirichlet and Neumann boundary conditions on the closed interval and with time-periodic right-hand side is proved. The nonlinear summand has a power-law growth.     

Approximation of the Hilbert Transform on the real semiaxis using Laguerre zeros

The authors propose two new algorithms for the computation of Cauchy principal value integrals on the real semiaxis. The proposed quadrature rules use zeros of Laguerre polynomials. Theoretical error estimates are proved and some numerical examples are showed.     

The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.     

On solutions of elliptic-type differential equations in a Banach space on a semiaxis

We describe all classical solutions of an abstract m-harmonic equation on (0,∞) and study their properties on this interval and in the neighborhood of the singular point 0.     

Weighted composition operator on the Fock space

We characterize the boundedness and compactness of a weighted composition operator on the Fock space. Our results use a certain integral transform. We also estimate the essential norm of a weighted compositon operator. The result could be extended to the higher-dimensional case.

     

Generalized Hilbert operator on the Dirichlet-type space

The boundedness of the generalized Hilbert operator on the Dirichlet-type space S_p when 0<p<1 is investigated.