Painless nonorthogonal expansions

Journal Article (Journal Article)

In a Hilbert spaced ℋ, discrete families of vectors {h } with the property that f = ∑ 〈 |f〉h 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 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. © 1966 American Institute of Physics. j j j j j

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