Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: An analytic continuation viewpoint - III

Forum Mathematicum

Volumn 9, Issue 2, 1997, Pages 165-191

  Bros, J ^a   Viano, G A ^b  

^a CEA SACLAY   (France)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031285539     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.1997.9.165     Document Type: Article

References (31)

1. Boas R. P.: "Entire Functions", Academic Press, New-York (1954).
2. Brocker Th. and Dijk T.: in "Groupes Compacts" Textbook-Springer (1985).
3. Bros J.: "Complexified de Sitter Space: Analytic Causal Kernels and Källen-Lehmann-Type Representation" in "Recent Advances in Field Theory", P. Binétruy, G. Girardi, P. Sorba Eds. (Nucl. Phys. B (Proc. Suppl.) 18B (1990)) p. 22-28.
4. Bros J. and Buchholz D.: "Fields at Finite Temperature; A General Study of the Two-Point Functions", in preparation.
5. Bros J., Gazeau J. P. and Moschella U.: "Quantum Field Theory on de Sitter Space", Phys. Rev. Lett. 73 (1994) p. 1746.
6. Bros J. and Moschella, U.: "Two-Point Functions and Quantum Fields in de Sitter Universe", Saclay Preprint SPhT/94/160, to appear in Reviews of Math. Phys.
7. Bros J. and Viano G. A.: "Connection Between the Algebra of Kernels on the Sphere and the Volterra Algebra on the One-Sheeted Hyperboloid: Holomorphic Perikernels", Bull. Soc. Math. France 120 (1992) p. 169-225.
8. Bros J. and Viano G. A.: "Complex Angular Momentum Analysis in Axiomatic Quantum Field Theory" in "Rigorous Methods in Particle Physics", S. Ciulli, F. Scheck, W. Thirring Eds. (Springer tracts in Mod. Phys. vol. 119 (1990)) p. 53-76.
9. Erdélyi A., Magnus W., Oberhettinger F. and Tricomi F. G.: "Tables of Integral Transforms", vol. II, McGraw-Hill, New-York (1954).
10. Erdélyi A., Magnus W., Oberhettinger F. and Tricomi F. G.: "Higher Transcendental Functions", vol. I, McGraw-Hill, New-York (1953).
11. Faraut J.: "Algèbre de Volterra et Transformation de Laplace Sphérique", Séminaire d'Analyse Harmonique de Tunis (1981) (Exposé 29).
12. Faraut J.: "Algèbres de Volterra et Transformation de Laplace Sphérique sur Certains Espaces Symétriques Ordonnés", Symposia Mathematica vol. XXIX (1984) p. 183-196.
13. Faraut J.: "Analyse Harmonique et Fonctions Spéciales", Ecole d'été d'Analyse Harmonique de Tunis (1984).
14. Faraut J., Hilgert J. and Olafsson G.: "Spherical Functions on Ordered Symmetric Spaces", Ann. Inst. Fourier, Grenoble 44 (1994) p. 927-966.
15. Faraut J. and Viano G. A.: "Volterra Algebra and the Bethe-Salpeter Equation", Journal of Math. Phys. 27, 3 (1986) p. 840-848.
16. Fioravanti R. and Viano G. A.: "On the Solution of the Inverse Scattering Problem at Fixed Energy, for the Class of Yukawian Potentials", Journal of Math. Phys. 36, 10 (1995) p. 5310-5339.
17. Froissart M.: "Asymptotic Behaviour and Subtractions in the Mandelstam Representation", Phys. Rev. 123, N 3 (1961) p. 1053-1057.
18. Gribov V. N.: "Partial Waves with Complex Angular Momenta and the Asymptotic Behaviour of the Scattering Amplitude", J. Exp. Theor. Phys. 14 (1962) p. 1395.
19. Helgason S.: "Differential Geometry and Symmetric Spaces", Academic Press. New-York (1962).
20. Huffman K.: "Banach Spaces of Analytic Functions", Prentice-Hall series in Modern Analysis, Englewood Cliffs N. J. (USA) (1962).
21. Khuri N. M.: "Regge Poles, Power Series and a Crossing-Symmetric Watson-Sommerfeld Transformation", Phys. Rev. 132 (1963) p. 914-926.
22. Leroy E.: "Sur les Séries Divergentes et les Fonctions Définies par un Développement de Taylor", Ann Faculté des Sci. Univ. de Toulouse 2 (1900) p. 317-430.
23. Martin A.: "Remarks on the Prolongation of a Scattering Amplitude in the Complex Angular Momentum Plane", Phys. Letters 1, 72 (1962) p. 72-75.
24. Painlevé P.: "Sur les Lignes Singulières des Fonctions Analytiques", Ann. Fac. Toulouse 2 (1888) p. 27.
25. Pham F: "Introduction à l'Etude Topologique des Singularités de Landau", Mémorial des Sciences Mathématiques 164, Gauthier-Villars, Paris (1967).
26. Poincaré H.: Œuvres, vol. 10. p. 94-203 (section 10).
27. Regge T.: "Introduction to Complex Orbital Momenta", Nuovo Cimento 14 (1959) 951-976.
28. Sommerfeld A.: "Partial Differential Equations in Physics", New-York (1949).
29. Stein E. M. and Wainger S.: "Analytic Properties of Expansions and Some Variants of Parseval-Plancherel Formula", Arkiv für Math. 5 (1963) p. 553-567.
30. Vilenkin N. Ja.: "Special Functions and the Theory of Group Representations", Amer. Math. Soc. Transi. 22, Providence R. I. (1968).
31. Watson G. N.: "The Diffraction of Electric Waves by the Earth", Proc. Roy. Soc., London 95 (1918) p. 83-99.