Kernels of unbounded Toeplitz operators and factorization of symbols

2020/04/21 by Câmara, M. Cristina, Malheiro, M. Teresa, Partington, Jonathan R. · 1 citation
#45E10 #47A68 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2004.09985

Abstract

We consider kernels of unbounded Toeplitz operators in H^p(\mathbb C⁺) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in H^p(\mathbb C⁺), we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involving two different Hardy spaces and we establish relations between the kernels of two operators whose symbols differ by a factor which corresponds, in the unit circle, to a non-integer power of z. We apply the results to describe the kernels of Toeplitz operators with non-vanishing piecewise continuous symbols.

Cited by

• Maximal functions, conjugations and multipliers between Toeplitz kernels

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