Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

MATRICES OF TOEPLITZ OPERATORS ON HARDY SPACES OVER BOUNDED DOMAINS

  • Received : 2016.07.21
  • Accepted : 2016.11.07
  • Published : 2017.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

Keywords

References

  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. S. Bell, Ahlfors maps, the double of a domain, and complexity in potential theory and conformal mapping, J. Anal. Math. 78 (1999), 329-344. https://doi.org/10.1007/BF02791140
  4. A. Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/1964), 89-102.
  5. Y.-B. Chung, Classification of Toeplitz Operators on Hardy spaces of bounded domains in the plane, Math. Notes (to appear).
  6. P. R. Garabedian, Schwarz's lemma and the Szego kernel function, Trans. Amer. Math. Soc. 67 (1949), 1-35.