Toeplitz Operators whose Symbols Are Borel Measures

摘要

In this paper, we are concerned with Toeplitz operators whose symbols are complex Borel measures. When a complex Borel measure on the unit circle is given, we give a formal definition of a Toeplitz operator with symbol , as an unbounded linear operator on the Hardy space. We then study various properties of . Among them, there is a theorem that the domain of is represented by a trichotomy. Also, it was shown that if the domain of contains at least one polynomial, then is densely defined. In addition, we give evidence for the conjecture that with a singular measure reduces to a trivial linear operator.