In this paper, we introduce the notion of biorthogonal wavelet packets associated with nonuniform multiresoltion analysis and study their characteristics by means of Fourier transform. Three biorthogonal formulas regarding these wavelet packets are established. Moreover, it is shown how to obtain several new Riesz bases of the space (R) by constructing a series of subspaces of these nonuniform ...

In the study of Hilbert spaces of analytic functions, it is noticed that complete interpolating sequences and Riesz bases of reproducing kernels are dual notions. In this work we make this duality explicit by identifying sequences of complex numbers with linear operators.

The results which I will describe arise from joint work with Bill Moran, ru.rd with Dani Berend, Charles Pearce and Andy Pollington. The common theme is the formalism of Riesz product measures, for these have proved to be exceptionally useful in the study of normal numbers. Elsewhere in these proceedings, Tony Dooley describes some of our joint work on the related class of G-measures (G for Gib...