Cardinal Sine Series: Convergence and Uniqueness

Uniform convergence of single and double sine series and integrals

Convergence, Uniqueness, and Summability of Multiple Trigonometric Series

In this paper our primary interest is in developing further insight into convergence properties of multiple trigonometric series, with emphasis on the problem of uniqueness of trigonometric series. Let E be a subset of positive (Lebesgue) measure of the k dimensional torus. The principal result is that the convergence of a trigonometric series on E forces the boundedness of the partial sums alm...

The Sparse Cardinal Sine Decomposition applied to Stokes integral equations

Numerical simulations of two-phase flows driven by viscosity (e.g. for bubble motions in glass melting process) rely on the ability to efficiently compute the solutions to discretized Stokes equations. When using boundary element methods to track fluid interfaces, one usually faces the problem of solving linear systems with a dense matrix with a size proportional to the system number of degrees...

A Faber Series Approach to Cardinal Interpolation

For a compactly supported function <p in Rd we study quasiinterpolants based on point evaluations at the integer lattice. We restrict ourselves to the case where the coefficient sequence Xf, for given data /, is computed by applying a univariate polynomial q to the sequence <p\Zd , and then convolving with the data f\Z(¡ . Such operators appear in the well-known Neumann series formulation of qu...

Some New Existence, Uniqueness and Convergence Results for Fractional Volterra-Fredholm Integro-Differential Equations

This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on thei...