Painless nonorthogonal expansions

Published

Journal Article

In a Hilbert spaced ℋ, discrete families of vectors {hj} with the property that f = ∑j〈j|f〉h j for every f in ℋ are considered. This expansion formula is obviously true if the family is an orthonormal basis of ℋ, but also can hold in situations where the hj 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. © 1966 American Institute of Physics.

Full Text

Duke Authors

Cited Authors

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

Published Date

  • January 1, 1986

Published In

Volume / Issue

  • 27 / 5

Start / End Page

  • 1271 - 1283

International Standard Serial Number (ISSN)

  • 0022-2488

Digital Object Identifier (DOI)

  • 10.1063/1.527388

Citation Source

  • Scopus