122
F. Barbaresco
A B
C D
= g(u) = W N uW
−1
N =
Re(α + β) −Im(α − β)
Im(α + β) Re(α − β)
(5.A29)
[123, 37, 124]
References
1. Cartan, E.: Sur les invariants intégraux de certains espaces homogènes clos et les propriétés
topologiques de ces espaces. Ann. Soc. Pol. De Math. 8, 181–225 (1929)
2. Cartan, H.: Allocution de Monsieur Henri Cartan, colloques Jean-Louis Koszul. Annales de
l’Institut Fourier, tome 37(4), 1–4 (1987)
3. Koszul, J.L.: L’œuvre d’Élie Cartan en géométrie différentielle, in Élie Cartan, 1869-1951.
Hommage de l’Académie de la République Socialiste de Roumanie à l’occasion du centenaire de sa naissance. Comprenant les communications faites aux séances du 4e Congrès du
Groupement des Mathématiciens d’Expression Latine, tenu à Bucarest en 1969, pp. 39–45.
Editura Academiei Republicii Socialiste Romania, Bucharest (1975)
4. Koszul, J.L.: Interview for “Institut Joseph Fourier” 50th birthday in 2016: video. https://
www.youtube.com/watch?v=AzK5K7Q05sw
5. Siegel, C.L.: Über der analytische Theorie der quadratischen Formen. Ann. Math. 36, 527–606
(1935)
6. Siegel, C.L.: Symplectic geometry. Am. J. Math. 65, 1–86 (1943)
7. Hua, L.K.: Harmonic Analysis of Functions of Several Complex Variables in the Classical
Domains. American Mathematical Society, Providence, RI, USA (1963)
8. Lichnerowicz, A.: Espaces homogènes Kähleriens. In: Colloque de Géométrie Différentielle;
Publication du CNRSP, Paris, France, pp. 171–184 (1953)
9. Berezin, F.: Quantization in complex symmetric spaces. Izv. Akad. Nauk SSSR Ser. Math. 9,
363–402 (1975)
10. Vesentini, E.: Geometry of homogeneous bounded domains, Springer-Verlag 2011, reprint of
the 1rst Ed. C.IM.E., Ed. Cremonese, Roma 1968
11. Sampieri, U.: A generalized exponential map for an affinely homogeneous cone, Atti
della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali.
Rendiconti Lincei. Matematica e Applicazioni, Serie 8, Vol. 75, n.6, pp. 320–330 (1983)
12. Sampieri, U.: Lie group structures and reproducing kernels on homogeneous siegel domains.
Annali di Matematica 152(1), 1–19 (1988)
13. Fréchet, M.: Sur l’extension de certaines évaluations statistiques au cas de petits échantillons.
Revue de l’Institut International de Statistique 11(3/4), 182–205 (1943)
14. Rao, C.R.: Information and the accuracy attainable in the estimation of statistical parameters.
Bull. Calcutta Math. Soc. 37, 81–89 (1945)
15. Chentsov, N.N.: Statistical Decision Rules and Optimal Inferences, Transactions of Mathematics Monograph, American Mathematical Society, Providence, RI, USA, Vol. 53 (1982)
16. Balian, R., Alhassid, Y., Reinhardt, H.: Dissipation in many-body systems: A geometric
approach based on information theory. Phys. Rep. 131, 1–146 (1986)
17. Balian, R.: The entropy-based quantum metric. Entropy 16, 3878–3888 (2014)
18. Gromov, M.: Convex sets and Kähler manifolds, In: Advances in Differential Geometry and
Topology; Tricerri, F. (Ed.), pp. 1–38. World Scientific, Singapore, Singapore (1990)
19. Gromov, M.: In a search for a structure, Part 1: On entropy, 23 June 2012 . http://www.ihes.
fr/~gromov/PDF/structre-serch-entropy-july5-2012.pdf
20. Gromov, M.: Gromov Six Lectures on Probability, Symmetry, Linearity. October 2014,
Jussieu, November 6th, 2014; Lecture Slides & video of Gromov lectures on youtube:
http://www.ihes.fr/~gromov/PDF/probability-huge-Lecture-Nov-2014.pdf; https://www.you
tube.com/watch?v=hb4D8yMdov4
F. Barbaresco
A B
C D
= g(u) = W N uW
−1
N =
Re(α + β) −Im(α − β)
Im(α + β) Re(α − β)
(5.A29)
[123, 37, 124]
References
1. Cartan, E.: Sur les invariants intégraux de certains espaces homogènes clos et les propriétés
topologiques de ces espaces. Ann. Soc. Pol. De Math. 8, 181–225 (1929)
2. Cartan, H.: Allocution de Monsieur Henri Cartan, colloques Jean-Louis Koszul. Annales de
l’Institut Fourier, tome 37(4), 1–4 (1987)
3. Koszul, J.L.: L’œuvre d’Élie Cartan en géométrie différentielle, in Élie Cartan, 1869-1951.
Hommage de l’Académie de la République Socialiste de Roumanie à l’occasion du centenaire de sa naissance. Comprenant les communications faites aux séances du 4e Congrès du
Groupement des Mathématiciens d’Expression Latine, tenu à Bucarest en 1969, pp. 39–45.
Editura Academiei Republicii Socialiste Romania, Bucharest (1975)
4. Koszul, J.L.: Interview for “Institut Joseph Fourier” 50th birthday in 2016: video. https://
www.youtube.com/watch?v=AzK5K7Q05sw
5. Siegel, C.L.: Über der analytische Theorie der quadratischen Formen. Ann. Math. 36, 527–606
(1935)
6. Siegel, C.L.: Symplectic geometry. Am. J. Math. 65, 1–86 (1943)
7. Hua, L.K.: Harmonic Analysis of Functions of Several Complex Variables in the Classical
Domains. American Mathematical Society, Providence, RI, USA (1963)
8. Lichnerowicz, A.: Espaces homogènes Kähleriens. In: Colloque de Géométrie Différentielle;
Publication du CNRSP, Paris, France, pp. 171–184 (1953)
9. Berezin, F.: Quantization in complex symmetric spaces. Izv. Akad. Nauk SSSR Ser. Math. 9,
363–402 (1975)
10. Vesentini, E.: Geometry of homogeneous bounded domains, Springer-Verlag 2011, reprint of
the 1rst Ed. C.IM.E., Ed. Cremonese, Roma 1968
11. Sampieri, U.: A generalized exponential map for an affinely homogeneous cone, Atti
della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali.
Rendiconti Lincei. Matematica e Applicazioni, Serie 8, Vol. 75, n.6, pp. 320–330 (1983)
12. Sampieri, U.: Lie group structures and reproducing kernels on homogeneous siegel domains.
Annali di Matematica 152(1), 1–19 (1988)
13. Fréchet, M.: Sur l’extension de certaines évaluations statistiques au cas de petits échantillons.
Revue de l’Institut International de Statistique 11(3/4), 182–205 (1943)
14. Rao, C.R.: Information and the accuracy attainable in the estimation of statistical parameters.
Bull. Calcutta Math. Soc. 37, 81–89 (1945)
15. Chentsov, N.N.: Statistical Decision Rules and Optimal Inferences, Transactions of Mathematics Monograph, American Mathematical Society, Providence, RI, USA, Vol. 53 (1982)
16. Balian, R., Alhassid, Y., Reinhardt, H.: Dissipation in many-body systems: A geometric
approach based on information theory. Phys. Rep. 131, 1–146 (1986)
17. Balian, R.: The entropy-based quantum metric. Entropy 16, 3878–3888 (2014)
18. Gromov, M.: Convex sets and Kähler manifolds, In: Advances in Differential Geometry and
Topology; Tricerri, F. (Ed.), pp. 1–38. World Scientific, Singapore, Singapore (1990)
19. Gromov, M.: In a search for a structure, Part 1: On entropy, 23 June 2012 . http://www.ihes.
fr/~gromov/PDF/structre-serch-entropy-july5-2012.pdf
20. Gromov, M.: Gromov Six Lectures on Probability, Symmetry, Linearity. October 2014,
Jussieu, November 6th, 2014; Lecture Slides & video of Gromov lectures on youtube:
http://www.ihes.fr/~gromov/PDF/probability-huge-Lecture-Nov-2014.pdf; https://www.you
tube.com/watch?v=hb4D8yMdov4