Toeplitz Operators Defined by Piecewise Continuous Matrix Functions

1993 ◽  
pp. 623-651
Author(s):  
I. Gohberg ◽  
M. A. Kaashoek ◽  
S. Goldberg
Keyword(s):  
Toeplitz Operators ◽  
Matrix Functions ◽  
Piecewise Continuous

scholarly journals Block Toeplitz operators with frequency-modulated semi-almost periodic symbols

2003 ◽  
Vol 2003 (34) ◽  
pp. 2157-2176 ◽  
Author(s):  
A. Böttcher ◽  
S. Grudsky ◽  
I. Spitkovsky
Keyword(s):  
Toeplitz Operator ◽  
Frequency Modulation ◽  
Real Line ◽  
Matrix Function ◽  
Toeplitz Operators ◽  
Matrix Functions ◽  
Almost Periodic ◽  
The Matrix ◽  
Matrix Symbol ◽  
Block Toeplitz Operators

This paper is concerned with the influence of frequency modulation on the semi-Fredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphismαof the real line that ensure the following: ifbbelongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix functions) and the Toeplitz operator generated by the matrix functionb(x)is semi-Fredholm, then the Toeplitz operator with the matrix symbolb(α(x))is also semi-Fredholm.

scholarly journals Kernels of Unbounded Toeplitz Operators and Factorization of Symbols

2020 ◽  
Vol 76 (1) ◽  
Author(s):  
M. C. Câmara ◽  
M. T. Malheiro ◽  
J. R. Partington
Keyword(s):  
Unit Circle ◽  
Hardy Spaces ◽  
Toeplitz Operators ◽  
Integer Power ◽  
Piecewise Continuous ◽  
Toeplitz Kernel

AbstractWe consider kernels of unbounded Toeplitz operators in $$H^p({\mathbb {C}}^{+})$$ H p ( C + ) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in $$H^p({\mathbb {C}}^{+})$$ H p ( 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.

scholarly journals Toeplitz operators with piecewise continuous symbols on the Hardy space $H^1$

2019 ◽  
Vol 57 (2) ◽  
pp. 429-435
Author(s):  
Santeri Miihkinen ◽  
Jani Virtanen
Keyword(s):  
Hardy Space ◽  
Toeplitz Operators ◽  
Piecewise Continuous

Toeplitz Operators Defined by Rational Matrix Functions

1993 ◽  
pp. 583-622
Author(s):  
I. Gohberg ◽  
M. A. Kaashoek ◽  
S. Goldberg
Keyword(s):  
Toeplitz Operators ◽  
Matrix Functions ◽  
Rational Matrix
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