B-Splines and orthonormal sets in Paley- Wiener space
Ahmed I. Zayed · Birkhäuser Boston eBooks · 1999
It is known that the cardinal B-splines can be used to generate a multiresolution analysis, and hence an orthonormal wavelet basis for $${{L}^{2}}(\mathbb{R}) $$ . We show that they can also be used to generate orthonormal sets, as well as, frames in the Paley-Wiener space $$B_{\sigma }^{2} $$ , which is also known as the space of bandlimited functions with bandwidth σ. A new orthonormal set of functions in $$B_{\sigma }^{2} $$ , obtained from one single function by translating it by integer multiples of 2π/σ is given explicitly in terms of Young’s function that was introduced by W. H. Young in 1912.