Zonal spherical function

노트

말뭉치

1. For zonal spherical functions see Spherical harmonics.
2. Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.
3. The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.
4. For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.
5. Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.

메타데이터

위키데이터

• ID : Q8073863

Spacy 패턴 목록

• [{'LOWER': 'cohen'}, {'OP': '*'}, {'LOWER': 'lenstra'}, {'LEMMA': 'heuristic'}]
• [{'LOWER': 'cohen'}, {'OP': '*'}, {'LEMMA': 'Lenstra'}]
• [{'LOWER': 'zonal'}, {'LOWER': 'spherical'}, {'LEMMA': 'function'}]

노트

말뭉치

1. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions.
2. The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group.
3. Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.
4. The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.
5. For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.
6. Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.
7. I tried to rotate zonal spherical function, projected onto spherical harmonic basis.
8. For zonal spherical functions see Spherical harmonics.
9. But to determine the explicitform of zonal spherical functions and the Plancherel measure, it seems necessary toknow the (infinite) matrix of this Fourier transformation more explicitly.
10. 3 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).
11. 4 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).

메타데이터

위키데이터

• ID : Q8073863

Spacy 패턴 목록

• [{'LOWER': 'cohen'}, {'OP': '*'}, {'LOWER': 'lenstra'}, {'LEMMA': 'heuristic'}]
• [{'LOWER': 'cohen'}, {'OP': '*'}, {'LEMMA': 'Lenstra'}]
• [{'LOWER': 'zonal'}, {'LOWER': 'spherical'}, {'LEMMA': 'function'}]

노트

말뭉치

1. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions.
2. The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group.
3. Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.
4. The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.
5. For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.
6. Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.
7. I tried to rotate zonal spherical function, projected onto spherical harmonic basis.
8. For zonal spherical functions see Spherical harmonics.
9. A more common usage of the phrase "spherical function" is as follows.
10. These solutions include the spherical functions associated with irreducible unitary representations.
11. S. ICHIRO SATAKE Theory of spherical functions on reductive algebraic groups over p-adic elds Publications mathmatiques de lI.H..
12. 69INTRODUCTIONThe theory of spherical functions on semi-simple Lie groups has been developedby Gelfand, Neumark, Harish-Chandra, Godement and others.
13. But to determine the explicitform of zonal spherical functions and the Plancherel measure, it seems necessary toknow the (infinite) matrix of this Fourier transformation more explicitly.
14. For g,eG, /eJf01, we put(5.7) (T,V)(^=/(^)-Then we have:248THEORY OF SPHERICAL FUNCTIONS 25PROPOSITION 5.1.
15. Am I simply making mistakes in my computation, or is there something wrong in this approach for spherical functions?
16. 3 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).
17. 4 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).
18. Let us recall rst what is a spherical function for a Gelfand pair.
19. Z G where is a bounded spherical function (m is a Haar measure on the group G, which is unimodular since (G, K) is a Gelfand pair).
20. We will denote the spherical functions of positive type for the Gelfand pair (G, K) (; x) ( , x G).
21. In the same way the spherical dual is identied with the set of spherical functions of positive type.
22. We present a sparse analytic representation for spherical functions, in- cluding those expressed in a spherical harmonic (SH) expansion, that is amenable to fast and accurate rotation on the GPU.
23. We present an alternative basis for spherical functions based on rotated zonal harmonic (ZH) lobes.
24. Let f () be a spherical function, with = (x, y, z) = (, ) S2, and and are spherical (lat-long) coordinates of point (x, y, z) on the spheres surface, S2.
25. The process of representing a spherical function, with an initial SH coefcient vector f , in the RZHB with a new coefcient vector z is called Zonal Harmonic Factorization (ZHF).

메타데이터

위키데이터

• ID : Q8073863

Spacy 패턴 목록

• [{'LOWER': 'spherical'}, {'LEMMA': 'function'}]
• [{'LOWER': 'zonal'}, {'LOWER': 'spherical'}, {'LEMMA': 'function'}]