The use of Volterra filters in practical applications is often limited by their high computational burden. To cope with this problem, many strategies for implementing Volterra filters with reduced complexity have been proposed in the open literature. Some of these strategies are based on reduced-rank approaches obtained by defining a matrix of filter coefficients and applying the singular value...

Bernstein polynomials have been recently used for the solution of some linear and non-linear differential equations, both partial and ordinary, by Bhatta and Bhatti [1] and Bhatti and Bracken [2]. Also these have been used to solve some classes of inegral equations of both first and second kinds, by Mandal and Bhattacharya [3]. These were further used to solve a Cauchy singular integro-differen...

Although various operators in the space of functions bounded variation have been studied by quite a few authors, no simple necessary and sufficient conditions guaranteeing compactness linear integral acting such spaces known. The aim paper is to fully characterize class kernels which generate compact BV-space. Using this characterization we show that certain weakly singular convolution (such as...