Analytic Subordination Consequences of Free Markovianity

Analytic Subordination Consequences of Free Markovianity

In [4], under some easy to remove genericity assumptions, we proved the analytic subordination of the Cauchy transforms of distributions GμX+Y and GμX for a pair of freely independent self-adjoint random variables X, Y . We used this to obtain inequalities among p-norms of densities of distributions, free entropies and Riesz energies. This was followed by P.Biane’s discovery [1] that subordinat...

Subordination Properties for Certain Analytic Functions

A. A. Attiya,1, 2 Nak Eun Cho,3 and M. A. Kutbi4 1Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura 35516, Egypt 2Department of Mathematics, Teachers’ College in Abha, King Khalid University, Abha, P.O. Box 249, Saudi Arabia 3Department of Applied Mathematics, Pukyong National University, Pusan 608-737, South Korea 4Department of Mathematics, Faculty of Science, Ki...

On Certain Subclasses of Analytic Functions Defined by Differential Subordination

Differential subordination for classes of normalized analytic functions 1

We determine the sufficient conditions for subordination for new classes of normalized analytic functions with applications in fractional calculus in complex domain. 2010 Mathematics Subject Classification: 34G10, 26A33, 30C45.

Subordination Results for Certain Classes of Analytic Functions

In the present paper, we derive some subordination results for certain classes of analytic functions by making use of a subordination theorem. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.