Math @ Duke

Publications [#287126] of Ingrid Daubechies
Papers Published
 Daubechies, I; Grossmann, A; Meyer, Y, Painless nonorthogonal expansions,
Journal of Mathematical Physics, vol. 27 no. 5
(January, 1986),
pp. 12711283, AIP Publishing, ISSN 00222488 [doi]
(last updated on 2019/05/26)
Abstract: In a Hilbert spaced ℋ, discrete families of vectors {hj} with the property that f = ∑j〈jf〉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 WeylHeisenberg coherent states, based on certain (nonGaussian) 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.


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