Toeplitz operators with semi-almost periodic symbols on spaces with Muckenhoupt weight

1994 ◽  
Vol 18 (3) ◽  
pp. 261-276 ◽  
Author(s):  
A. B�ttcher ◽  
Yu. I. Karlovich ◽  
I. M. Spitkovsky
Keyword(s):  
Toeplitz Operators ◽  
Muckenhoupt Weight ◽  
Almost Periodic

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 Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols

2001 ◽  
Vol 130 (5) ◽  
pp. 1365-1370 ◽  
Author(s):  
Leiba Rodman ◽  
Ilya M. Spitkovsky ◽  
Hugo J. Woerdeman
Keyword(s):  
Toeplitz Operators ◽  
Almost Periodic

Toeplitz operators with frequency modulated semi-almost periodic symbols

2001 ◽  
Vol 7 (5) ◽  
pp. 523-535 ◽  
Author(s):  
A. Böttcher ◽  
S. Grudsky ◽  
I. Spitkovsky
Keyword(s):  
Toeplitz Operators ◽  
Almost Periodic

Fredholm Toeplitz Operators and Slow Oscillation

1980 ◽  
Vol 32 (5) ◽  
pp. 1058-1071 ◽  
Author(s):  
S. C. Power
Keyword(s):  
Toeplitz Operators ◽  
Continuous Functions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Necessary And Sufficient Criteria ◽  
Symbol Function ◽  
Oscillating Functions ◽  
Necessary And Sufficient ◽  
Slowly Oscillating Functions

The purpose of this paper is to show how Fred hoi m criteria for Toeplitz operators, whose symbols lie in an algebra,A, may often be generalized to cover a larger symbol algebra generated by A and SO, the slowly oscillating functions. Mere A and SO are algebras of continuous functions on the real line, so that we are concerned principally with the effect of a single discontinuity in the symbol function.We shall treat the cases when A is the almost periodic functions, the semi-almost periodic functions and the multiplicatively periodic functions. Sufficient criteria for Fredholmness are obtained in Section 5. The more difficult task of establishing necessary and sufficient criteria is only achieved here for the slowly oscillating almost periodic functions and this is done in Section 6.

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