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Publications [#287091] of Ingrid Daubechies

Papers Published

  1. Daubechies, I; Grossmann, A; Meyer, Y, Painless nonorthogonal expansions (January, 2009), pp. 372-384
    (last updated on 2017/12/17)

    Abstract:
    © 2006 by Princeton University Press. All Rights Reserved. In a Hilbert space {Hilbert space}, discrete families of vectors {hj} with the property that f = Σ J < h J |f > h J 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 j 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.

 

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