scholarly journals On the Weyl Matrix Balls Associated with Nondegenerate Matrix-Valued Carathéodory Functions

1993 ◽  
Vol 12 (2) ◽  
pp. 239-261 ◽  
Author(s):  
B. Fritzsche ◽  
B. Kirstein
Keyword(s):  
Nondegenerate Matrix ◽  
Weyl Matrix ◽  
Carathéodory Functions

The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*

2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar
Keyword(s):  
Triangle Inequality ◽  
Starlike Functions ◽  
Sharp Bound ◽  
The Novel ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Lemniscate Of Bernoulli ◽  
Carathéodory Functions ◽  
The Right

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

scholarly journals Differential Inequalities and Carathéodory Functions

1997 ◽  
Vol 212 (1) ◽  
pp. 324-332 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Akira Ikeda ◽  
Naoya Koike ◽  
Yoshiaki Ota ◽  
Hitoshi Saitoh
Keyword(s):  
Differential Inequalities ◽  
Carathéodory Functions

scholarly journals Finite-Gap CMV Matrices: Periodic Coordinates and a Magic Formula

2020 ◽  
Author(s):  
Jacob S Christiansen ◽  
Benjamin Eichinger ◽  
Tom VandenBoom
Keyword(s):  
Unit Circle ◽  
Functional Model ◽  
Rational Functions ◽  
Almost Periodic ◽  
Absolutely Continuous ◽  
Magic Formula ◽  
Carathéodory Functions ◽  
Möbius Transforms ◽  
Rotational Phase ◽  
Isospectral Torus

Abstract We prove a bijective unitary correspondence between (1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum ${\textsf{E}}$ and (2) special periodic block-CMV matrices satisfying a Magic Formula. This latter class arises as ${\textsf{E}}$-dependent operator Möbius transforms of certain generating CMV matrices that are periodic up to a rotational phase; for this reason we call them “MCMV.” Such matrices are related to a choice of orthogonal rational functions on the unit circle, and their correspondence to the isospectral torus follows from a functional model in analog to that of GMP matrices. As a corollary of our construction we resolve a conjecture of Simon; namely, that Caratheodory functions associated to such CMV matrices arise as quadratic irrationalities.

scholarly journals Sufficient conditions for strongly Carathéodory functions

2011 ◽  
Vol 62 (8) ◽  
pp. 2978-2987 ◽  
Author(s):  
Hitoshi Shiraishi ◽  
Shigeyoshi Owa ◽  
H.M. Srivastava
Keyword(s):  
Sufficient Conditions ◽  
Carathéodory Functions
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