Cardinal translation invariant Tchebycheffian B-splines

Cardinal Tchebycheffian B-splines, defined by weight functions of the form with , are investigated. It is shown that these B-splines are translation invariant, have a geometric representation and satisfy a generalized Hermite-Genocchi formula. For pure exponential weight functions the above results lead to a product type expression for the Fourier transform of the cardinal exponential B-splines, showing that these functions are convolutions of lower order ones. Similar conclusions are obtained for the corresponding Greens' functions.