On the Growth of the Resolvent of a Toeplitz Operator
Copyright policy )On the Growth of the Resolvent of a Toeplitz Operator
Summary: We study the growth of the resolvent of a Toeplitz operator \(T_b\), defined on the Hardy space, in terms of the distance to its spectrum \(\sigma(T_b)\). We are primarily interested in the case when the symbol \(b\) is a Laurent polynomial (i.e., the matrix \(T_b\) is banded). We show that for an arbitrary such symbol the growth of the resolvent is quadratic (3.1), and under certain additional assumption it is linear (2.1). We also prove the quadratic growth of the resolvent for a certain class of non-rational symbols.
Integral operators, Hardy spaces, Toeplitz operator, resolvent growth, regular Laurent polynomials, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Laurent polynomial with Jordan property, Hardy space
Integral operators, Hardy spaces, Toeplitz operator, resolvent growth, regular Laurent polynomials, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Laurent polynomial with Jordan property, Hardy space
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