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Painless nonorthogonal expansions. (English) Zbl 0608.46014
In a Hilbert space , discrete families of vectors {h j } with the property that f= j <h j |f>h j for every f in are considered. This expansion formula is obviously true if the family is an orthonormal basis of , 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.

MSC:
46C99Inner product spaces, Hilbert spaces
46B15Summability and bases in normed spaces