대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제54권6호
  • /
  • Pages.2013-2027
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  • 2017
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SPECIAL ORTHONORMAL BASIS FOR L2 FUNCTIONS ON THE UNIT CIRCLE

  • 투고 : 2016.08.24
  • 심사 : 2016.12.26
  • 발행 : 2017.11.30
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초록

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

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참고문헌

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  2. S. Bell, The Szego projection and the classical objects of potential theory in the plane, Duke Math. J. 64 (1991), no. 1, 1-26. https://doi.org/10.1215/S0012-7094-91-06401-X
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  4. Y.-B. Chung, Classification of Toeplitz operators on Hardy spaces of bounded domains in the plane, Math. Notes 101 (2017), no. 3, 529-541. https://doi.org/10.1134/S0001434617030142
  5. Y.-B. Chung, Matrices of Toeplitz operators on Hardy spaces over bounded domains, Bull. Korean Math. Soc. 54 (2017), no. 4, 1421-1441. https://doi.org/10.4134/BKMS.B160611
  6. Y.-B. Chung, Toeplitz operators on Hardy and Bergman spaces over bounded domains in the plane, Honam Math. J., to appear.