Kernels of unbounded Toeplitz operators and factorization of symbols

We consider kernels of unbounded Toeplitz operators in Hp(C+) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in Hp(C+), we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involvin...

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Bibliographic Details
Main Author: Câmara, M. C. (author)
Other Authors: Malheiro, M. Teresa (author), Partington, J. R. (author)
Format: article
Language:eng
Published: 2021
Subjects:
Toeplitz operators
generalized factorization
Wiener–Hopf operators
Ciências Naturais::Matemáticas
Science & Technology
Online Access:http://hdl.handle.net/1822/72386
Country:Portugal
Oai:oai:repositorium.sdum.uminho.pt:1822/72386
Description
Summary:We consider kernels of unbounded Toeplitz operators in Hp(C+) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in Hp(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.

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