DOI QR코드

DOI QR Code

SPECIAL ORTHONORMAL BASIS FOR L2 FUNCTIONS ON THE UNIT CIRCLE

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

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.

키워드

참고문헌

  1. S. Bell, Solving the Dirichlet problem in the plane by means of the Cauchy integral, Indiana Univ. Math. J. 39 (1990), no. 4, 1355-1371. https://doi.org/10.1512/iumj.1990.39.39060
  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
  3. A. Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/1964), 89-102.
  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.