5 papers
The Cauchy dual subnormality problem via de Branges-Rovnyak spaces
Sameer Chavan, Soumitra Ghara, Md Ramiz Reza
The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a -isometry is subnormal. In this paper, we address this problem for cyclic -isometries…
Dirichlet-type spaces on the unit ball and joint 2-isometries
Sameer Chavan, Rajeev Gupta, Md. Ramiz Reza
We obtain a formula that relates the spherical moments of the multiplication tuple on a Dirichlet-type space to a complex moment problem in several variables. This can be seen as t…
Hausdorff moment sequences induced by rational functions
Md. Ramiz Reza, Genkai Zhang
We study the Hausdorff moment problem for a class of sequences, namely where is a rational function in the complex plane. We obtain a necessary cond…
Curvature Inequalities and Extremal Operators
Gadadhar Misra, Md. Ramiz Reza
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operato…
Curvature inequalities for operators in the Cowen-Douglas class of a planar domain
Md. Ramiz Reza
Fix a bounded planar domain If an operator in the Cowen-Douglas class admits the compact set as a spectral set, then the curvature inequality $\mathcal…