On the convergence of a lacunary Fourier series and its conjugate series.
On the convergence of biorthogonal series corresponding to nonselfadjoint Sturm-Liouville operator with discontinuous coefficients.
On the convergence of Fourier series.
On the convergence of moments in the CLT for triangular arrays with an application to random polynomials
We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.
On the convolution of a probability measure.
On the (C,α≥0,β≥0)-summability of double orthogonal series
On the decay properties of the Franklin analyzing wavelet
On the degree of approximation by Gauss Weierstrass integrals.
On the Degree of Approximation by the Operators of de la Vallée Poussin.
On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense
For real functions of bounded variation in the Hardy sense, -periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.
On the degree of convergence of Borel and Euler means of trigonometric series
On the degree of strong approximation of continuous functions by special matrix.
On the degree of strong approximation of integrable functions.
On the degree of strong approximation of integrable functions in Stepanov sense
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
On the denseness of Jacobi polynomials.
On the direct kernels with respect to the Walsh-Kaczmarz system.
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
On the discrete wavelet transform of stochastic processes.
On the distribution of zeros of exponential polynomials
On the distribution on the roots of polynomials
Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.