Abstract

The Einstein-Podolsky-Rosen entangled state representation is applied to studying the admissibility condition of mother wavelets for complex wavelet transforms, which leads to a family of new mother wavelets. Mother wavelets thus are classified as the Hermite-Gaussian type for real wavelet transforms and the Laguerre-Gaussian type for the complex case.

© 2007 Optical Society of America

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References

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  1. M. A. Pinsky, Introduction to Fourier Analysis and Wavelets (Brooks/Cole, 2002).
  2. I. Daubechies, in CBMS-NSF Series in Applied Mathematics (SIAM, 1992).
  3. H.-Y. Fan and H.-L. Lu, Opt. Lett. 31, 407 (2006).
    [CrossRef]
  4. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
    [CrossRef]
  5. H.-Y. Fan and J. R. Klauder, Phys. Rev. A 49, 704 (1994).
    [CrossRef]
  6. H.-Y. Fan and Y. Fan, Phys. Rev. A 54, 958 (1996).
    [CrossRef]
  7. H.-Y. Fan, H. R. Zaidi, and J. R. Klauder, Phys. Rev. D 35, 1831 (1987).
    [CrossRef]
  8. H.-Y. Fan, J. Opt. B Quantum Semiclassical Opt. 5, R147 (2003).
    [CrossRef]
  9. H.-Y. Fan, H.-L. Lu, and Y. Fan, Ann. Phys. 321, 480 (2006).
  10. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
    [CrossRef]
  11. J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, 1985).
  12. A. Erdelyi, Higher Transcendental Functions, The Bateman Manuscript Project (McGraw-Hill, 1953).
  13. H.-Y. Fan, Phys. Lett. A 303, 311 (2002).
  14. R. Loudon and P. L. Knight, J. Mod. Opt. 34, 709 (1987).
  15. D. F. Walls, Nature 306, 141 (1983).
    [CrossRef]
  16. H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
    [CrossRef]

2006 (2)

H.-Y. Fan, H.-L. Lu, and Y. Fan, Ann. Phys. 321, 480 (2006).

H.-Y. Fan and H.-L. Lu, Opt. Lett. 31, 407 (2006).
[CrossRef]

2003 (1)

H.-Y. Fan, J. Opt. B Quantum Semiclassical Opt. 5, R147 (2003).
[CrossRef]

2002 (1)

H.-Y. Fan, Phys. Lett. A 303, 311 (2002).

1996 (1)

H.-Y. Fan and Y. Fan, Phys. Rev. A 54, 958 (1996).
[CrossRef]

1994 (1)

H.-Y. Fan and J. R. Klauder, Phys. Rev. A 49, 704 (1994).
[CrossRef]

1987 (2)

H.-Y. Fan, H. R. Zaidi, and J. R. Klauder, Phys. Rev. D 35, 1831 (1987).
[CrossRef]

R. Loudon and P. L. Knight, J. Mod. Opt. 34, 709 (1987).

1983 (1)

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

1976 (1)

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

1963 (1)

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Daubechies, I.

I. Daubechies, in CBMS-NSF Series in Applied Mathematics (SIAM, 1992).

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Erdelyi, A.

A. Erdelyi, Higher Transcendental Functions, The Bateman Manuscript Project (McGraw-Hill, 1953).

Fan, H.-Y.

H.-Y. Fan and H.-L. Lu, Opt. Lett. 31, 407 (2006).
[CrossRef]

H.-Y. Fan, H.-L. Lu, and Y. Fan, Ann. Phys. 321, 480 (2006).

H.-Y. Fan, J. Opt. B Quantum Semiclassical Opt. 5, R147 (2003).
[CrossRef]

H.-Y. Fan, Phys. Lett. A 303, 311 (2002).

H.-Y. Fan and Y. Fan, Phys. Rev. A 54, 958 (1996).
[CrossRef]

H.-Y. Fan and J. R. Klauder, Phys. Rev. A 49, 704 (1994).
[CrossRef]

H.-Y. Fan, H. R. Zaidi, and J. R. Klauder, Phys. Rev. D 35, 1831 (1987).
[CrossRef]

Fan, Y.

H.-Y. Fan, H.-L. Lu, and Y. Fan, Ann. Phys. 321, 480 (2006).

H.-Y. Fan and Y. Fan, Phys. Rev. A 54, 958 (1996).
[CrossRef]

Glauber, R. J.

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Klauder, J. R.

H.-Y. Fan and J. R. Klauder, Phys. Rev. A 49, 704 (1994).
[CrossRef]

H.-Y. Fan, H. R. Zaidi, and J. R. Klauder, Phys. Rev. D 35, 1831 (1987).
[CrossRef]

J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, 1985).

Knight, P. L.

R. Loudon and P. L. Knight, J. Mod. Opt. 34, 709 (1987).

Loudon, R.

R. Loudon and P. L. Knight, J. Mod. Opt. 34, 709 (1987).

Lu, H.-L.

H.-Y. Fan and H.-L. Lu, Opt. Lett. 31, 407 (2006).
[CrossRef]

H.-Y. Fan, H.-L. Lu, and Y. Fan, Ann. Phys. 321, 480 (2006).

Pinsky, M. A.

M. A. Pinsky, Introduction to Fourier Analysis and Wavelets (Brooks/Cole, 2002).

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Skargerstam, B. S.

J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, 1985).

Walls, D. F.

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Yuen, H. P.

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Zaidi, H. R.

H.-Y. Fan, H. R. Zaidi, and J. R. Klauder, Phys. Rev. D 35, 1831 (1987).
[CrossRef]

Ann. Phys. (1)

H.-Y. Fan, H.-L. Lu, and Y. Fan, Ann. Phys. 321, 480 (2006).

J. Mod. Opt. (1)

R. Loudon and P. L. Knight, J. Mod. Opt. 34, 709 (1987).

J. Opt. B Quantum Semiclassical Opt. (1)

H.-Y. Fan, J. Opt. B Quantum Semiclassical Opt. 5, R147 (2003).
[CrossRef]

Nature (1)

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

H.-Y. Fan, Phys. Lett. A 303, 311 (2002).

Phys. Rev. (2)

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Phys. Rev. A (3)

H.-Y. Fan and J. R. Klauder, Phys. Rev. A 49, 704 (1994).
[CrossRef]

H.-Y. Fan and Y. Fan, Phys. Rev. A 54, 958 (1996).
[CrossRef]

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Phys. Rev. D (1)

H.-Y. Fan, H. R. Zaidi, and J. R. Klauder, Phys. Rev. D 35, 1831 (1987).
[CrossRef]

Other (4)

J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, 1985).

A. Erdelyi, Higher Transcendental Functions, The Bateman Manuscript Project (McGraw-Hill, 1953).

M. A. Pinsky, Introduction to Fourier Analysis and Wavelets (Brooks/Cole, 2002).

I. Daubechies, in CBMS-NSF Series in Applied Mathematics (SIAM, 1992).

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