On the kernel of a singular integral operator with shift

On the Kernel of a Singular Integral Operator with Non–carleman Shift and Conjugation

On the Hilbert space ̃L2(T) the singular integral operator with non-Carleman shift and conjugation K = P+ + (aI + AC)P− is considered, where P± are the Cauchy projectors, A = m ∑ j=0 ajU j , a,aj , j = 1,m , are continuous functions on the unit circle T , U is the shift operator and C is the operator of complex conjugation. Some estimates for the dimension of the kernel of the operator K are obt...

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...

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...

On the Volterra Integral Equation with Weakly Singular Kernel

The convexity of the integral operator on the class of the integral operator on the class B(mu,alpha)

In this paper, we study the convexity of the integral operator