Gabor Transformation on the Sphere and Its Inverse Transformation

Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We will consider the Gabor transformation for the square integrable function on the two-dimensional sphere and its inverse transformation. By using an integral over R3 we will give the inverse Gabor transformation concretely.

Keywords

Expansion formula Gabor transformation Sphere 

Mathematics Subject Classification (2010)

Primary 42C40; Secondary 33C50 

References

  1. 1.
    K. Fujita, Hilbert spaces related to harmonic functions. Tôhoku Math. J. 48, 149–163 (1996). doi:http://doi.org/10.2748/tmj/1178225416
  2. 2.
    K. Fujita, Gabor transformation on the circle, in Proceedings of the 2014 International Conference on Wavelet Analysis and Pattern Recognition (2014), pp. 122–126. doi:10.1109/ICWAPR2014.6961302
  3. 3.
    K. Fujita, Gabor transform of analytic functional on the sphere, in Current Trends in Analysis and Its Applications, Proceedings of the 9th ISAAC Congress, Kraków 2013 (Springer International Publishing, Cham, 2015), pp. 451–458. doi: 10.1007/978-3-319-12577-0_50 Google Scholar
  4. 4.
    M. Morimoto, Analytic Functionals on the Sphere, Translation of Mathematical Monographs, vol. 178 (American Mathematical Society, Providence, RI, 1998)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ToyamaToyamaJapan

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