Painless nonorthogonal expansions
- 1 May 1986
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (5), 1271-1283
- https://doi.org/10.1063/1.527388
Abstract
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.Keywords
This publication has 9 references indexed in Scilit:
- Transforms associated to square integrable group representations. I. General resultsJournal of Mathematical Physics, 1985
- Functions analytic on the half-plane as quantum mechanical statesJournal of Mathematical Physics, 1984
- Cycle-octave and related transforms in seismic signal analysisGeoexploration, 1984
- Decomposition of Hardy Functions into Square Integrable Wavelets of Constant ShapeSIAM Journal on Mathematical Analysis, 1984
- Square-integrable representations of non-unimodular groupsBulletin of the Australian Mathematical Society, 1976
- Proof of completeness of lattice states in therepresentationPhysical Review B, 1975
- On the completeness of the coherent statesReports on Mathematical Physics, 1971
- Continuous Representation Theory Using the Affine GroupJournal of Mathematical Physics, 1969
- A class of nonharmonic Fourier seriesTransactions of the American Mathematical Society, 1952