On Convergence of Orthogonal Expansion of a Function From the Class in the Eigenfunctions of a Differential Operator of the Third Order

We consider a third-order ordinary differential operator with summable coefficients. The absolute and uniform convergence of the orthogonal expansion of a function from the class in the eigenfunctionsof this operator is studied and the rate of uniform convergence of these expansions on is estimated

Absolute and Uniform Convergence of Spectral Expansion in the Eigenfunctions of a Third-Order Ordinary Differential Operator

In this paper studied the convergence of spectral expansions of functions of the class W1 1 ( ) G ,G= ( ) 0,1 in eigenfunctions of an ordinary differential operator of third order with integral coefficients. Sufficient conditions for absolute and uniform convergence are obtained and the rate of uniform convergence of these expansions on the interval G is found.

Riesz Inequality for the System of Root Functions of Second Order Ordinary Differential Operator

An ordinary differential operator of second order with coefficients is considered. The Riesz property of the system of root functions of the given operator is studied. The criterion of Bessel property in 2 L , of root functions system is established and use it to obtain sufficient conditions for the Riesz property of a system of normalized root functions of this operator in p L .

Absolute and uniform convergence of spectral expansion of the function from the class W1p(g), p > 1, in eigenfunctions of third order differential operator

We study an ordinary differential operator of third order and absolute and uniform convergence of spectral expansion of the function from the class W1p(G), G = (0,1), p > 1, in eigenfunctions of the operator. Uniform convergence rate of this expansion is estimated.

Spectral Curve of the Halphen Operator

The Halphen operator is a third-order operator of the formwhere g ≠ 2 mod(3), where the Weierstrass ℘-function satisfies the equationIn the equianharmonic case, i.e. g2 = 0, the Halphen operator commutes with some ordinary differential operator Ln of order n ≠ 0 mod(3). In this paper we find the spectral curve of the pair L3, Ln.

Some Applications of Ordinary Differential Operator to Certain Multivalent Functions

The aim of this paper is to apply the well-known ordinary differential operator to certain multivalent functions which are analytic in the certain domains of the complex plane and then to determine some criteria concerning analytic and geometric properties of the related complex functions.