The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C + (x), C − (x), S + (x), and S − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x r + and x r are evaluated. The Fresnel cosine integral C(x) is defined by C(x) = 2 π x 0 cos ...

Recently multiplicity M, K-regular, orthonormal wavelet bases (that have implications in transform coding applications) have been constructed by several authors 1, 2, 3]. This paper describes and parameterizes the cosine-modulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs (like in the general multiplicity 2 case in 4]), the scaling function uniquely determines the wavel...