Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results

2013 ◽  
Vol 66 (9) ◽  
pp. 1360-1438 ◽  
Author(s):  
Percy Deift ◽  
Alexander Its ◽  
Igor Krasovsky
Keyword(s):  
Ising Model ◽  
Toeplitz Matrices ◽  
Toeplitz Determinants

scholarly journals Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 181 ◽  
Author(s):  
Hari Srivastava ◽  
Qazi Ahmad ◽  
Nasir Khan ◽  
Nazar Khan ◽  
Bilal Khan
Keyword(s):  
Unit Disk ◽  
Toeplitz Matrices ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Conic Domain

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U . In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results.

scholarly journals Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
V. Radhika ◽  
S. Sivasubramanian ◽  
G. Murugusundaramoorthy ◽  
Jay M. Jahangiri
Keyword(s):  
Unit Disk ◽  
Toeplitz Matrices ◽  
Open Unit ◽  
Open Unit Disk ◽  
Toeplitz Determinants ◽  
Sharp Bounds ◽  
The Family ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

Let R denote the family of functions f(z)=z+∑n=2∞anzn of bounded boundary rotation so that Ref′(z)>0 in the open unit disk U={z:z<1}. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions f∈R.

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