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SYMMETRY OF SPECIAL COMPOSITION OPERATORS ON THE HARDY SPACE

  • Received : 2023.05.11
  • Accepted : 2023.07.16
  • Published : 2024.03.20

Abstract

We consider a special orthonormal basis for the Hardy space of the unit disc to compute the matrix representations of the composition operators with respect to the basis particulary associated to two symbols which are the inverse and the origin symmetry of the Riemann self map in the unit disc, and then we find a certain symmetry of the matrices.

Keywords

References

  1. Steven R. Bell, Complexity of the classical kernel functions of potential theory, Indiana Univ. Math. J. 44 (1995), no. 4, 1337-1369.  https://doi.org/10.1512/iumj.1995.44.2030
  2. Paul S. Bourdon and S. Waleed Noor, Complex symmetry of invertible composition operators, J. Math. Anal. Appl. 429 (2015), no. 1, 105-110.  https://doi.org/10.1016/j.jmaa.2015.04.008
  3. Y.-B. Chung, Classification of Toeplitz operators on Hardy spaces of bounded domains in the plane, Math. Notes 101 (2017), no. 3-4, 529-541.  https://doi.org/10.1134/S0001434617030142
  4. Y.-B. Chung, Special orthonormal basis for L2 functions on the unit circle, Bull. Korean Math. Soc. 54 (2017), no. 6, 2013-2027. 
  5. Y.-B. Chung, The matrix representation of a composition operator on the Hardy space, Bull. Korean Math. Soc. 59 (2022), no. 5, 1119-1129. 
  6. Carl C. Cowen and Barbara D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. 
  7. Sivaram K. Narayan, Daniel Sievewright, and Maria Tjani, Complex symmetric composition operators on weighted Hardy spaces, Proc. Amer. Math. Soc. 148 (2020), no. 5, 2117-2127. https://doi.org/10.1090/proc/14909