Spirals in Hilbert space: With an application in information theory

Expositiones Mathematicae

Volumn 23, Issue 1, 2005, Pages 23-45

  Fuglede, Bent ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Helix; Hilbert space embedding; Information theory; Jensen Shannon kernel; Negative definite kernel; Schoenberg's theorem; Spiral

Indexed keywords

EID: 18644366659     PISSN: 07230869     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.exmath.2005.01.014     Document Type: Article

References (12)

1. S. Bochner, Vorlesungen über Fouriersche Integrale, Akademische Verlagsgesellschaft, Leipzig, 1932.
2. C. Berg, J.P.R. Christensen, P. Ressel, Harmonic Analysis on Semigroups, Springer, New York, 1984.
3. n, et formule de Lévy-Khinchine, Bull. Sci. Math. 88 (1964) 3-30.
4. A. Erdélyi, et al., Higher Transcendental Functions, vol. I, McGraw-Hill, New York, 1954.
5. A. Erdélyi, et al., Higher Transcendental Functions, vol. II, McGraw-Hill, New York, 1955.
6. A.N. Kolmogorov, Curves in Hilbert space which are invariant with respect to a one-parameter group of motions, Doklady Akad. Nauk 26 (1940) 6-9 (in Russian).
7. P. Masani, On helixes in Hilbert space, I, Theory Probab. Appl. 17 (1972) 1-19.
8. J. von Neumann, I.J. Schoenberg, Fourier integrals and metric geometry, Trans. Amer. Math. Soc. 50 (1941) 226-251.
9. I.J. Schoenberg, Metric spaces and positive definite functions, Trans. Amer. Math. Soc. 44 (1938) 522-536.
10. M.H. Stone, Linear Transformations in Hilbert Space, American Mathematical Society Colloquium Publications XV, American Mathematical Society, New York, 1932.
11. M.H. Stone, On one-parameter unitary groups in Hilbert space, Ann. Math. 33 (1932) 643-648.
12. F. TopsØe, Jensen-Shannon divergence and norm-based measures of discrimination and variation, preprint 2003.