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Painless nonorthogonal expansions
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.
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Cited by
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Metadata
- Authors
- Daubechies, I., Grossmann, A., & Meyer, Y.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1986-05-01
- Volume
- 27
- Issue
- 5
- Pages
- 1271-1283
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2087377426
- Cited by
- 1,290
- References
- 0
- FWCI
- 13.67
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Painless nonorthogonal expansions. https://app.cochat.ai/papers/10.1063/1.527388
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- Daubechies, I., Grossmann, A., & Meyer, Y. (1986). Painless nonorthogonal expansions. Journal of Mathematical Physics. https://doi.org/10.1063/1.527388
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