Math @ Duke

Publications [#287091] of Ingrid Daubechies
Papers Published
 Daubechies, I; Grossmann, A; Meyer, Y, Painless nonorthogonal expansions
(January, 2009),
pp. 372384
(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 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.


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