Spherical functions on hyperboloids
Web1. apr 1973 · INTRODUCTION The theory of spherical harmonics establishes a three way equiv- alence between (a) irreducible representations of the rotation (or orthogonal) group … Web1. máj 2000 · The main his tools were so called spherical distributions and decomposition of the Laplace-Beltrami operator. Also there are numerous papers of Molchanov, van Dijk, …
Spherical functions on hyperboloids
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Web19. apr 2011 · Abstract The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space... Web19. apr 2008 · A function u ∈ C 2 (S p,q) is called a spherical harmonic 1 of d egr e e ρ if u is the restriction to S p,q of a function in H ρ . Let H ρ denote the space of spherical
Web15. jún 1997 · Spherical functions on hyperboloids Mat. Sbornik, 99 ( 1976), pp. 139 - 161 View in Scopus Google Scholar 11 Math. USSR—Sbornik, 28 ( 1976), pp. 119 - 139 12 V.F … Web20. mar 2008 · Abstract: Eigenfunctions of the Laplace-Beltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple self-contained proof of Laplace's …
Web10. júl 2000 · Maximal functions: Spherical means Proc. Nat. Acad. Sci. U.S.A., 73 ( 1976), pp. 2174 - 2175 CrossRef View in Scopus Google Scholar 19 E.M. Stein Harmonic Analysis, Princeton Univ. Press, Princeton ( 1993) Google Scholar 20 D. Tataru, Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation, preprint, 1997. Webtypes of “spherical functions” as basis functions for irreducible representations of the Lorentz group, realized on O(3,1) hyperboloids. This turned out to be a pathbreaking article that lead to many interesting developments in the representation theory of noncompact groups and their physical applications.
WebIn particular, these investigations have examined the relationship between the separation of variables for the Helmholtz equations on the four homogeneous spaces: two-dimensional sphere S 2 ,...
WebGiven a functionf(p a p b) of the scalar product of two timelike, lightlike or space-like four-vectors it can be expanded in terms of the productsY σ P (p a) * Y σ P (p b) of spherical functions on the (p a) 2 and (p b) 2 hyperboloids. Simple formulas for the evaluation of the expansion coefficients are derived. The expansions are presented in the form of addition … arsenal\\u0027s b0WebInvariant subspaces of functions and the poisson transformation for hyperboloids I. I. Shitikov Siberian Mathematical Journal volume 29 , pages 476–482 ( 1988 ) Cite this article ban aeroxWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. Eigenfunctions of the Laplace-Beltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple self-contained proof of Laplace’s integral for a Legendre function is obtained. arsenal\u0027s b2Web1. feb 2001 · Math. Ann. 319, 215–234 (2001) Mathematische Annalen Digital Object Identifier (DOI) 10.1007/s002080000146 Determinantal formulas for zonal spherical functions on hyperboloids J.F. van Diejen · A.N. Kirillov Received November 18, 1999 / Published online October 30, 2000 – Springer-Verlag 2000 Abstract. We construct … banaer英文Webusing series expansions with either spheroidal or spherical functions have been proposed [11], [12], [13]. Unfortunately ... [0,∞) and one-sheeted hyperboloids of revolution (Fig.1, right). d/2 is the semidistance between focal points. We are interested in the modes inside a spheroid adjacent to its surface in the equatorial plane. It is ... ban aerox depan belakangWebThe hyperboloid has the symmetry group SO (1, 4). It can be covered by various different coordinates. The time-dependent coordinate systems include all three FRW cases: closed, flat and open slicings. The closed universe map covers the whole hyperboloid (4.1) where the line element on S2 is , see Fig. 9. Sign in to download full-size image Fig. 9. arsenal\u0027s biWebhyperboloid is given by the equation u2 = 1 and the point $ corresponds to a point on this hyperboloid with coordinates: -b c 1 + p2 6 p 'U = c 1 - p2 ., 1 - p2 ) (7) The region p2 < 1 is mapped on the upper sheet while p2 > 1 is mapped on the lower one. We shall need the following relations. banafair bananen