# Painless nonorthogonal expansions

Journal Article (Chapter)

In a Hilbert space {Hilbert space}, discrete families of vectors {hj} with the property that f = Σ h for every f in {Hilbert space} are considered. This expansion formula is obviously true if the family is an orthonorma1 basis of {Hilbert space}, but also can hold in situations where the h are not mutually orthogonal and are "overcomplete." The two classes of examples studied here are (i) appropriate sets of Weyl-Heisenberg coherent states, based on certain (non-Gaussian) fiducial vectors, and (ii) analogous families of affine coherent states. It is believed, that such "quasiorthogonal expansions" will be a useful tool in many areas of theoretical physics and applied mathematics. J J J j

### Duke Authors

### Cited Authors

- Daubechies, I; Grossmann, A; Meyer, Y

### Published Date

- January 10, 2009

### Start / End Page

- 372 - 384

### Citation Source

- Scopus