Title: Peter-Weyl Theorem for Homogeneous Spaces of Compact Groups
Author(s): Arash Ghaani Farashahi
Pages: 22-31
Cite as:
Arash Ghaani Farashahi, Peter-Weyl Theorem for Homogeneous Spaces of Compact Groups, Int. J. Anal. Appl., 13 (1) (2017), 22-31.

Abstract


This paper presents a structured formalism for a constructive generalization of the Peter-Weyl Theorem over homogeneous spaces of compact groups. Let H be a closed subgroup of a compact group G and µ be the normalized G-invariant measure on the compact left coset space G/H. We then present an abstract T H -version of the Peter-Weyl Theorem for the Hilbert function space L2 (G/H,µ).

Full Text: PDF

 

References


  1. G.B. Folland, A course in Abstract Harmonic Analysis, CRC press, 1995.

  2. A. Ghaani Farashahi, Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups, Groups, Geometry, Dynamics, in press.

  3. A. Ghaani Farashahi, Abstract Plancherel (trace) formulas over homogeneous spaces of compact groups, Canadian Mathematical Bulletin, doi:10.4153/CMB-2016-037-6.

  4. A. Ghaani Farashahi, Abstract harmonic analysis of wave packet transforms over locally compact abelian groups, Banach J. Math. Anal. 11 (1) (2017), 50-71.

  5. A. Ghaani Farashahi, Abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups, J. Aust. Math. Soc., 101 (2) (2016) 171-187.

  6. A. Ghaani Farashahi, Abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor, J. Korean Math. Soc., 101 (2) (2016), 171-187.

  7. A. Ghaani Farashahi, Convolution and involution on function spaces of homogeneous spaces, Bull. Malays. Math. Sci. Soc. (36) (4) (2013), 1109-1122.

  8. A. Ghaani Farashahi, Abstract non-commutative harmonic analysis of coherent state transforms, Ph.D. thesis, Ferdowsi University of Mashhad (FUM), Mashhad 2012.

  9. E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol 1, 1963.

  10. E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol 2, 1970.

  11. V. Kisil, Calculus of operators: covariant transform and relative convolutions, Banach J. Math. Anal. 8 (2) (2014), 156-184.

  12. V. Kisil, Geometry of Möbius transformations. Elliptic, parabolic and hyperbolic actions of SL 2 (R), Imperial College Press, London, 2012.

  13. V. Kisil, Relative convolutions. I. Properties and applications, Adv. Math. 147 (1) (1999), 35-73.

  14. G.J. Murphy, C*-Algebras and Operator theory, Academic Press, INC, 1990.

  15. F. Peter and H. Weyl, Die Vollstndigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Math. Ann., 97 (1927) 737-755.