Integral operators with Green's function type kernel

Integral Operators Induced by the Fock Kernel

We study the L boundedness and find the norm of a class of integral operators induced by the reproducing kernel of Fock spaces over C.

The Convergence of Family of Integral Operators with Positive Kernel

Majorization of Singular Integral Operators with Cauchy Kernel on L

Let a, b, c and d be functions in L = L(T, dθ/2π), where T denotes the unit circle. Let P denote the set of all trigonometric polynomials. Suppose the singular integral operators A and B are defined by A = aP + bQ and B = cP + dQ on P, where P is an analytic projection and Q = I − P is a co-analytic projection. In this paper, we use the Helson–Szegő type set (HS)(r) to establish the condition o...

On the Hardy-type Integral Operators in Banach Function Spaces

Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.

An effective method for approximating the solution of singular integral equations with Cauchy kernel type

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...