【摘要】 本文讨论了Toeplitz算子在Hardy空间H1(S)上的Fredholm性质.证明了在单位球面S上处处不为零的连续函数φ具有对数有界平均振动时,以其为符号的Toeplitz算子Tφ是Fredholm算子,并且此时Tφ的指标为零.更多还原

【Abstract】 In this paper,we study the Fredholm properties of Toeplitz operators on H1(S).We prove that if a nowhere vanishing symbol function φ satisfies a slightly stronger condition than φ is continuous on S,then Tφ is Fredholm on H1(S),where S is the unit sphere of Cn.Moreover,when n > 1,we have the index of Tφ is zero.更多还原