QUANTIZATION OPERATORS ON QUADRICS

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概要

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• 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 $ L_2 (S^n) $ 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.

著者

• FURUTANI Kenro

  DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AND TECHNOLOGY SCIENCE UNIVERSITY OF TOKYO

• BAUER Wolfram

  Fachbereich Mathematik und Informatik Johannes-Gutenberg Universitat

関連論文

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