Folding Operators, Wilson Bases, and Zak Transforms

K. Bittner

Department of Mathematics and Computer Science, University of Missouri -- St. Louis, 8001 Natural Bridge Road, St. Louis, MO 63121-4499, USA
email: bittner@math.umsl.edu

In this chapter biorthogonal Wilson bases for $L^2([0,N])$ are investigated. The approach uses the even, periodic extension of functions defined on the interval. Starting from Wilson bases for periodic functions, Wilson bases for even, periodic functions are constructed. The basis functions are finally restricted to a suitable interval. Dual bases and Riesz bounds are given explicitly. The construction is based on a Zak transform for periodic functions and an unfolding operator for periodic Wilson bases. Fast algorithms for analysis and synthesis are described.