"Zonal spherical function"의 두 판 사이의 차이
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* [{'LOWER': 'cohen'}, {'OP': '*'}, {'LEMMA': 'Lenstra'}] | * [{'LOWER': 'cohen'}, {'OP': '*'}, {'LEMMA': 'Lenstra'}] | ||
* [{'LOWER': 'zonal'}, {'LOWER': 'spherical'}, {'LEMMA': 'function'}] | * [{'LOWER': 'zonal'}, {'LOWER': 'spherical'}, {'LEMMA': 'function'}] | ||
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| + | == 노트 == | ||
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| + | ===말뭉치=== | ||
| + | # Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions.<ref name="ref_a3254751">[https://www.sciencedirect.com/science/article/pii/S0001870803003530 Quantum zonal spherical functions and Macdonald polynomials]</ref> | ||
| + | # The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group.<ref name="ref_8b1a5a04">[https://en.wikipedia.org/wiki/Zonal_spherical_harmonics Zonal spherical harmonics]</ref> | ||
| + | # Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.<ref name="ref_bbc7de78">[https://en.wikipedia.org/wiki/Zonal_spherical_function Zonal spherical function]</ref> | ||
| + | # The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.<ref name="ref_bbc7de78" /> | ||
| + | # For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.<ref name="ref_bbc7de78" /> | ||
| + | # Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.<ref name="ref_bbc7de78" /> | ||
| + | # I tried to rotate zonal spherical function, projected onto spherical harmonic basis.<ref name="ref_677b2b6d">[https://ask.sagemath.org/question/48775/rotation-of-zonal-spherical-functions/ Rotation of zonal spherical functions [closed]]</ref> | ||
| + | # For zonal spherical functions see Spherical harmonics.<ref name="ref_dd393068">[https://encyclopediaofmath.org/wiki/Spherical_functions Encyclopedia of Mathematics]</ref> | ||
| + | # 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.<ref name="ref_51df46c4">[http://www.numdam.org/article/PMIHES_1963__18__5_0.pdf Publications mathématiques de l’i.h.é.s.]</ref> | ||
| + | # 3 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).<ref name="ref_3ed88387">[https://www.math.fsu.edu/~vlasiuk/pdf/glazyrin.pdf Mapping to the space of spherical harmonics]</ref> | ||
| + | # 4 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).<ref name="ref_3ed88387" /> | ||
| + | ===소스=== | ||
| + | <references /> | ||
2021년 2월 22일 (월) 20:20 판
노트
말뭉치
- For zonal spherical functions see Spherical harmonics.[1]
- Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.[2]
- The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.[2]
- For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.[2]
- Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.[2]
소스
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
- Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions.[1]
- The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group.[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.[3]
- For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.[3]
- Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.[3]
- I tried to rotate zonal spherical function, projected onto spherical harmonic basis.[4]
- For zonal spherical functions see Spherical harmonics.[5]
- 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.[6]
- 3 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).[7]
- 4 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).[7]
소스
- ↑ Quantum zonal spherical functions and Macdonald polynomials
- ↑ Zonal spherical harmonics
- ↑ 3.0 3.1 3.2 3.3 Zonal spherical function
- ↑ Rotation of zonal spherical functions [closed]
- ↑ Encyclopedia of Mathematics
- ↑ Publications mathématiques de l’i.h.é.s.
- ↑ 7.0 7.1 Mapping to the space of spherical harmonics