## Painless nonorthogonal expansions

Publication
, Journal Article

Daubechies, I; Grossmann, A; Meyer, Y

Published in: Journal of Mathematical Physics

January 1, 1986

In a Hilbert spaced ℋ, discrete families of vectors {hj} with the property that f = ∑j〈j|f〉h j 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. © 1966 American Institute of Physics.

### Duke Scholars

##### Altmetric Attention Stats

##### Dimensions Citation Stats

## Published In

Journal of Mathematical Physics

## DOI

## ISSN

0022-2488

## Publication Date

January 1, 1986

## Volume

27

## Issue

5

## Start / End Page

1271 / 1283

## Related Subject Headings

- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences

### Citation

APA

Chicago

ICMJE

MLA

NLM

Daubechies, I., Grossmann, A., & Meyer, Y. (1986). Painless nonorthogonal expansions.

*Journal of Mathematical Physics*,*27*(5), 1271–1283. https://doi.org/10.1063/1.527388Daubechies, I., A. Grossmann, and Y. Meyer. “Painless nonorthogonal expansions.”

*Journal of Mathematical Physics*27, no. 5 (January 1, 1986): 1271–83. https://doi.org/10.1063/1.527388.Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions. Journal of Mathematical Physics. 1986 Jan 1;27(5):1271–83.

Daubechies, I., et al. “Painless nonorthogonal expansions.”

*Journal of Mathematical Physics*, vol. 27, no. 5, Jan. 1986, pp. 1271–83.*Scopus*, doi:10.1063/1.527388.Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions. Journal of Mathematical Physics. 1986 Jan 1;27(5):1271–1283.

## Published In

Journal of Mathematical Physics

## DOI

## ISSN

0022-2488

## Publication Date

January 1, 1986

## Volume

27

## Issue

5

## Start / End Page

1271 / 1283

## Related Subject Headings

- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences