Spherical functions on hyperboloids
WebMAXIMAL OPERATORS ON HYPERBOLOIDS A. EL KOHEN INTRODUCTION In a paper in 1976 [8], E. M. Stein introduced and studied the following maxi mal function: mfix) = sup I … Web24. mar 2024 · A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the perpendicular bisector to the line between the foci (Hilbert and Cohn-Vossen 1991, p. 11). A hyperboloid of one sheet is also obtained as the envelope of a cube rotated about a …
Spherical functions on hyperboloids
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Webhyperboloid 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. 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 … WebWe investigate properties of some spherical functions defined on hyperbolic groups using boundary representations on the Gromov boundary endowed with the Patterson–Sullivan …
WebThe spherical functions are given in a basis defined by the two-dimensional momentum (N 1 +M 2,N 2 −M 1) of horospheric translations where N and M denote the generators of … WebCiteSeerX - 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.
WebFor the hyperboloid X = G/H, where G = SO 0 ( p, q) and H = SO 0 ( p, q − 1), we define canonical representations R λ,ν λ ∈ ℂ, ν = 0, 1, as the restrictions to G of representations …
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. sushi house telegraph menuWebInvariant subspaces of functions and the poisson transformation for hyperboloids I. I. Shitikov Siberian Mathematical Journal volume 29 , pages 476–482 ( 1988 ) Cite this article sushi house telegraph canyon chula vistaIn geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an … Zobraziť viac Cartesian coordinates for the hyperboloids can be defined, similar to spherical coordinates, keeping the azimuth angle θ ∈ [0, 2π), but changing inclination v into hyperbolic trigonometric functions: One-surface … Zobraziť viac Imaginary hyperboloids are frequently found in mathematics of higher dimensions. For example, in a pseudo-Euclidean space one … Zobraziť viac • Weisstein, Eric W. "Hyperboloid". MathWorld. Zobraziť viac Hyperboloid of one sheet Lines on the surface • A hyperboloid of one sheet contains two pencils of lines. It is a doubly ruled surface. If the hyperboloid has the equation are contained in … Zobraziť viac In 1853 William Rowan Hamilton published his Lectures on Quaternions which included presentation of biquaternions. The following … Zobraziť viac • de Sitter space • Ellipsoid • List of surfaces • Paraboloid / Hyperbolic paraboloid Zobraziť viac six rings from nowhereWebDeterminantal formulas for zonal spherical functions on hyperboloids @article{vanDiejen2001DeterminantalFF, title={Determinantal formulas for zonal spherical functions on hyperboloids}, author={J. F. van Diejen and Anatol N. Kirillov}, journal={Mathematische Annalen}, year={2001}, volume={319}, pages={215-234} } sixrivers.caWeb18. okt 2007 · Spherical functions on hyperboloids Authors: Vladimir Fedorovich Molchanov Tambov State University named after G.R. Derzhavin Abstract Spherical (zonal) functions … sushi house temucoWebIn this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order q -difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. six river farm facebookWebIn 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 ,... six river national forest