Abstract
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = zng(z)(n ≥ 1), g(z) = b0 + b1\( z^{p_1 } \)+b2\( z^{p_2 } \)+···, bk ≠ 0(k = 0, 1, 2, ...), our main result is Open image in new window (Mf) = Open image in new window (\( M_{z^n } \))∩ Open image in new window (Mg) = Open image in new window (\( M_{z^s } \)), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D.
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