New class of uncertainty relations for partially coherent light

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 1, Issue 7, 1984, Pages 711-715

  Bastiaans, Martin J ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

PARTIALLY COHERENT LIGHT;

LIGHT;

EID: 0021455314     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.1.000711     Document Type: Article

References (21)

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13. F. Riesz and B. S. Nagy, Functional Analysis (Ungar, New York, 1955).
14. A. J. E. M. Janssen, "Positivity of weighted Wigner distributions," SIAM J. Math. Anal. 12, 752-758 (1981).
15. The proof in Appendix A is due to M. L. J. Hautus, Technische Hogeschool Eindhoven, Eindhoven, The Netherlands (personal communication).
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18. The nonincreasing behavior of jlq can be proved by showing that its derivative is nonpositive, indeed, with f (t) = t log t (t ≥ 0) a convex function, we have which is nonpositive by means of Ref. 20, Sec. 1.4.7, Eq. (1).
19. M. Marcus and H. Minc, Introduction to Linear Algebra (Macmillan, New York, 1965), Sec. 3.5, Theorem 5.9.
20. D. S. Mitrinovic, Analytic Inequalities (Springer-Verlag, Berlin, 1970).
21. The proof in Appendix C is partly due to J. Boersma, Technische Hogeschool Eindhoven, Eindhoven, The Netherlands (personal communication).