# FREDHOLM TOEPLITZ OPERATORS ON THE DIRICHLET SPACES OF THE POLYDISK

• Na, Kyunguk (Peace and Liberal Arts College, Mathematics Hanshin University)
• Accepted : 2019.11.06
• Published : 2020.03.31

#### Abstract

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

#### Acknowledgement

Supported by : Hanshin University

#### References

9. W. Rudin, Function Theory in the Unit Ball of $C^n$, Springer-Verlag, New York, 1980.