In a Hilbert space ℋ, discrete families of vectors {hj} with the property that f=∑j〈hj‖ f〉hj 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 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.
Gaussian expansions of ground-state Hartree—Fock solutions for the first-row atoms are determined by a self-consistent-field minimization of atomic energies. Wavefunctions are c...
Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible ...
Recent extensions of the DMol3 local orbital density functional method for band structure calculations of insulating and metallic solids are described. Furthermore the method fo...
Suppose a discrete-time signal S(t), 0/spl les/t<N, is a superposition of atoms taken from a combined time-frequency dictionary made of spike sequences 1/sub {t=/spl tau/}/ and ...
A density-functional method for calculations on periodic systems (periodicity in one, two, or three dimensions) is presented in which all aspects of numerical precision are effi...
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