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UNIQUENESS OF TOEPLITZ OPERATOR IN THE COMPLEX PLANE

Chung, Young-Bok

  • Received : 2009.11.13
  • Accepted : 2009.12.14
  • Published : 2009.12.25

Abstract

We prove using the Szeg$\H{o}$ kernel and the Garabedian kernel that a Toeplitz operator on the boundary of $C^{\infty}$ smoothly bounded domain associated to a smooth symbol vanishes only when the symbol vanishes identically. This gives a generalization of previous results on the unit disk to more general domains in the plane.

Keywords

Szeg$\H{o}$ kernel;Toeplitz operator;Garabedian kernel

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