Details
| Original language | English |
|---|---|
| Pages (from-to) | 221-258 |
| Number of pages | 38 |
| Journal | Kyushu journal of mathematics |
| Volume | 62 |
| Issue number | 1 |
| Publication status | Published - 2008 |
| Externally published | Yes |
Abstract
We explain the construction of a Hilbert space on quadrics arising by the method of pairing polarizations. Then we introduce a family of measures and operators from function spaces on these quadrics to L2(S) which are defined by fiber integration. We compare the quantization operators and characterize them in the framework of pseudo-differential operator theory. An asymptotic property of the reproducing kernel of the Hilbert spaces consisting of holomorphic functions defined on quadrics is proved. This is a generalization of the Segal-Bargmann space and its reproducing kernel. Next we treat the case of the complex projective space and we explain that the space corresponding to the quadric is a matrix space consisting of rank-one complex matrices whose square is zero. Most of the theorems can be stated in the same way parallel to the sphere case.
Keywords
- Complex projective space, Geodesic flow, Geometric quantization, Hopf fibration, Kähler structure, Pairing of the polarizations, Reproducing kernel, Segal-Bargmann space, Sphere
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Kyushu journal of mathematics, Vol. 62, No. 1, 2008, p. 221-258.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantization Operators On Quadrics
AU - Bauer, Wolfram
AU - Furutani, Kenro
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - We explain the construction of a Hilbert space on quadrics arising by the method of pairing polarizations. Then we introduce a family of measures and operators from function spaces on these quadrics to L2(S) which are defined by fiber integration. We compare the quantization operators and characterize them in the framework of pseudo-differential operator theory. An asymptotic property of the reproducing kernel of the Hilbert spaces consisting of holomorphic functions defined on quadrics is proved. This is a generalization of the Segal-Bargmann space and its reproducing kernel. Next we treat the case of the complex projective space and we explain that the space corresponding to the quadric is a matrix space consisting of rank-one complex matrices whose square is zero. Most of the theorems can be stated in the same way parallel to the sphere case.
AB - We explain the construction of a Hilbert space on quadrics arising by the method of pairing polarizations. Then we introduce a family of measures and operators from function spaces on these quadrics to L2(S) which are defined by fiber integration. We compare the quantization operators and characterize them in the framework of pseudo-differential operator theory. An asymptotic property of the reproducing kernel of the Hilbert spaces consisting of holomorphic functions defined on quadrics is proved. This is a generalization of the Segal-Bargmann space and its reproducing kernel. Next we treat the case of the complex projective space and we explain that the space corresponding to the quadric is a matrix space consisting of rank-one complex matrices whose square is zero. Most of the theorems can be stated in the same way parallel to the sphere case.
KW - Complex projective space
KW - Geodesic flow
KW - Geometric quantization
KW - Hopf fibration
KW - Kähler structure
KW - Pairing of the polarizations
KW - Reproducing kernel
KW - Segal-Bargmann space
KW - Sphere
UR - http://www.scopus.com/inward/record.url?scp=44949237162&partnerID=8YFLogxK
U2 - 10.2206/kyushujm.62.221
DO - 10.2206/kyushujm.62.221
M3 - Article
AN - SCOPUS:44949237162
VL - 62
SP - 221
EP - 258
JO - Kyushu journal of mathematics
JF - Kyushu journal of mathematics
SN - 1340-6116
IS - 1
ER -