Powers of the Pick function and applications

2002 ◽  
Vol 13 (1) ◽  
pp. 35-44
Author(s):  
Pavel G. Todorov
Keyword(s):  
Pick Function

scholarly journals Application of the Pick Function in the Lieb Concavity Theorem for Deformed Exponentials

2021 ◽  
Vol 6 (1) ◽  
pp. 20
Author(s):  
Guozeng Yang ◽  
Yonggang Li ◽  
Jing Wang ◽  
Huafei Sun
Keyword(s):  
Important Application ◽  
Exterior Algebra ◽  
Concave Functions ◽  
Pick Function

The Lieb concavity theorem, successfully solved in the Wigner–Yanase–Dyson conjecture, is an important application of matrix concave functions. Recently, the Thompson–Golden theorem, a corollary of the Lieb concavity theorem, was extended to deformed exponentials. Hence, it is worthwhile to study the Lieb concavity theorem for deformed exponentials. In this paper, the Pick function is used to obtain a generalization of the Lieb concavity theorem for deformed exponentials, and some corollaries associated with exterior algebra are obtained.

The Markov chain associated to a Pick function

2000 ◽  
Vol 118 (4) ◽  
pp. 439-454 ◽  
Author(s):  
Gérard Letac ◽  
Dhafer Malouche
Keyword(s):  
Markov Chain ◽  
Pick Function

scholarly journals An Inductive Julia-Carathéodory Theorem for Pick Functions in Two Variables

2018 ◽  
Vol 61 (3) ◽  
pp. 647-660 ◽  
Author(s):  
J. E. Pascoe
Keyword(s):  
Analytic Function ◽  
Half Plane ◽  
Real Line ◽  
Moment Theory ◽  
Representing Measure ◽  
Pick Functions ◽  
Upper Half Plane ◽  
Finite Measures ◽  
Carathéodory Theorem ◽  
Pick Function

AbstractClassically, Nevanlinna showed that functions from the complex upper half plane into itself which satisfy nice asymptotic conditions are parametrized by finite measures on the real line. Furthermore, the higher order asymptotic behaviour at infinity of a map from the complex upper half plane into itself is governed by the existence of moments of its representing measure, which was the key to his solution of the Hamburger moment problem. Agler and McCarthy showed that an analogue of the above correspondence holds between a Pick function f of two variables, an analytic function which maps the product of two upper half planes into the upper half plane, and moment-like quantities arising from an operator theoretic representation for f. We apply their ‘moment’ theory to show that there is a fine hierarchy of levels of regularity at infinity for Pick functions in two variables, given by the Löwner classes and intermediate Löwner classes of order N, which can be exhibited in terms of certain formulae akin to the Julia quotient.

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