In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often...

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving...

particular fixed axis. The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry...

Spherical function can refer to Spherical harmonics Zonal spherical function This disambiguation page lists mathematics articles associated with the same...

investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly...

theory of differential equations. It is the special case for zonal spherical functions of the general Plancherel theorem for semisimple Lie groups, also...

space of S L ( 2 , R ) {\displaystyle SL(2,\mathbb {R} )} (see Zonal spherical function). Actually the Fourier transform on L 1 ( G / / K ) {\displaystyle...

asymptotic behavior of a zonal spherical function of a Lie group, and Harish-Chandra (1970) introduced a more general c-function called Harish-Chandra's...

his doctoral student Alan Graham Constantine. They appear as zonal spherical functions of the Gelfand pairs ( S 2 n , H n ) {\displaystyle (S_{2n},H_{n})}...

theory of SL2(R) Representations of the Lorentz group Stone–von Neumann theorem Unitary representation of a star Lie superalgebra Zonal spherical function...

arrangement of hyperplanes). Special hypergeometric functions occur as zonal spherical functions on Riemannian symmetric spaces and semi-simple Lie groups...

consequence of this expression for the Green's function is the Poisson integral formula. Let ρ, θ, and φ be spherical coordinates for the source point P. Here...

Mehler–Heine formula; and Mehler functions (conical functions), in connection with his utilization of Zonal spherical functions in Electromagnetic theory. Krause...

body: Functions of the form ϕ = R ( r ) Θ ( θ ) Φ ( φ ) {\displaystyle \phi =R(r)\,\Theta (\theta )\,\Phi (\varphi )} where (r, θ, φ) are the spherical coordinates...

Langlands program Kirillov orbit theory Discrete series representation Zonal spherical function "Noncommutative harmonic analysis: in honor of Jacques Carmona"...

is the Rossby parameter, k is the zonal wavenumber, and ℓ is the meridional wavenumber. It is noted that the zonal phase speed of Rossby waves is always...

the Schur functions in the case of root systems of type A. If q = 0 the Macdonald polynomials become the (rescaled) zonal spherical functions for a semisimple...

Schur functions, the Hall–Littlewood symmetric functions, the Jack symmetric functions, the zonal symmetric functions, the zonal spherical functions, and...

credited with the discovery that the Earth had a significant third degree zonal spherical harmonic in its gravitational field using Vanguard 1 satellite data...

Harmonic function Spherical harmonics Zonal spherical harmonics Multilinear polynomial Walsh, J. L. (1927). "On the Expansion of Harmonic Functions in Terms...

\cdot \mathbf {y} )} are spherical harmonics, when regarded as a function of x only. They are, in fact, exactly the zonal spherical harmonics, up to a normalizing...

MR 1913438 Letzter, G. (2003). "Quantum Symmetric Pairs and Their Zonal Spherical Functions". Transformation Groups. 8 (3): 261–291. arXiv:math/0204103. doi:10...

external waves, and the Hough functions degenerate to spherical functions; e.g., mode (1, −2) develops to the spherical function P 1 1 (θ), mode (2, 2) becomes...

of the Venera 4 to 7 probes were the first evidence of the existence of zonal winds with high speeds of up to 100 metres per second (330 ft/s, 362 km/h...

departures of it from spherical symmetry. From the point of view of satellite dynamics, of particular relevance are the so-called even zonal harmonic coefficients...

Over the years models consisting of an increasing but limited number of spherical harmonics have been produced. Maps produced have included free-air gravity...

cemented in the posterior element had 3 functions: to reduce the spherical aberration; reduce the overcorrected spherical-oblique aberration; and reduce the...

wave modes degenerate to the spherical functions Pnm with m a meridional wave number and n the zonal wave number (m = 0: zonal mean flow; m = 1: diurnal...

the Earth, including the antipodes, zonal maps showing the Ptolemaic climates derived from the concept of a spherical Earth and a diagram showing the Earth...

galaxy Zakharov system Zero-point energy ZETA (fusion reactor) Zonal and poloidal Zonal flow (plasma) Z Pulsed Power Facility G.S. Miller, E.E. Salpeter...