3 citations · 3 across the 8 of their papers we have counts for
8 papers
An example of a cyclic analytic -isometry with defect operator of rank , whose Cauchy dual is not subnormal
Saee A. Joshi, Geetanjali M. Phatak, Vinayak M. Sholapurkar
The Cauchy dual subnormality problem (CDSP, for short) asks whether the Cauchy dual of a isometry is subnormal. In this article, we provide a counter-example to CDSP by constru…
A solution to the Cauchy dual subnormality problem for a cyclic analytic -isometry with defect operator of rank two
Mandar Khasnis, Geetanjali Phatak, Vinayak Sholapurkar
The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a -isometry is subnormal. In this article, we prove that if is a sum of unit point mas…
Joint Complete Monotonicity of reciprocal of a polynomial in two variables
Mandar Khasnis, V. M. Sholapurkar
In this article, we study some special cases of the problem of classifying polynomials for which the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+…
Completely hyperexpansive operators with finite rank defect operator and de Branges-Rovnyak spaces
Saee A. Joshi, Vinayak M. Sholapurkar
The process of identifying a Dirichlet-type space for a positive, Borel measure , supported on the unit circle with a de Branges-Rovnyak space was initiated…
Cyclic Analytic 2-isometry of Finite Rank and Cauchy Dual Subnormality Problem
M. N. Khasnis, V. M. Sholapurkar
The Cauchy dual subnormality problem has attracted the attention of the researchers in recent years. In this article, we describe the problem and present a new counter example to t…
Weighted Translation Semigroups: Multivariable Case
Geetanjali M. Phatak, V. M. Sholapurkar
M. Embry and A. Lambert initiated the study of a weighted translation semigroup in with a view to explore a continuous analogue of a weigh…
An Analytic Model for left invertible Weighted Translation Semigroups
Geetanjali M. Phatak, V. M. Sholapurkar
M. Embry and A. Lambert initiated the study of a semigroup of operators indexed by a non-negative real number and termed it as weighted translation semigroup. The ope…
Hyperexpansive Weighted Translation Semigroups
Geetanjali M. Phatak, V. M. Sholapurkar
The weighted shift operators turn out to be extremely useful in supplying interesting examples of operators on Hilbert spaces. With a view to study a continuous analogue of weighte…