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Casimir Operator and Wavelet Transform

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Harmonic Analysis in China

Part of the book series: Mathematics and Its Applications ((MAIA,volume 327))

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Abstract

Let D be the unit disk in the complex plane equipped with the Lebesque measure dm(z). The Moebius group G = SU(1,1) consists of all 2 × 2 complex matrices

$$ g = \left( {\begin{array}{*{20}c} a \\ c \\ \end{array} \begin{array}{*{20}c} b \\ d \\ \end{array} } \right)a,b,c,d \in C $$

with \( c = \overline b ,d = \overline a ,ad - bc = 1. \)It acts on D via transformations

$$ z \to gz: = g(z) = \frac{{az + b}} {{cz + d}} $$

Research was supported in part by the National Natural Science Foundation of China

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Author information

Authors and Affiliations

  1. Deparment of mathematics, Peking University, China

    Qingtang Jiang & Lizhong Peng

Authors
  1. Qingtang Jiang
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  2. Lizhong Peng
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, China

    Minde Cheng

  2. Department of Mathematics, Zhongshan University, Guangzhou, China

    Dong-gao Deng

  3. Department of Mathematics, University of Science and Technology, Hefei, China

    Sheng Gong

  4. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon,Hong Kong, China

    Chung-Chun Yang

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© 1995 Springer Science+Business Media Dordrecht

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Jiang, Q., Peng, L. (1995). Casimir Operator and Wavelet Transform. In: Cheng, M., Deng, Dg., Gong, S., Yang, CC. (eds) Harmonic Analysis in China. Mathematics and Its Applications, vol 327. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0141-7_6

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  • DOI: https://doi.org/10.1007/978-94-011-0141-7_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4064-8

  • Online ISBN: 978-94-011-0141-7

  • eBook Packages: Springer Book Archive

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