arXiv subjects

Mandar Khasnis

Publications and source records attributed to Mandar Khasnis.

2 recordsLinked to original sources

arXiv2026

A solution to the Cauchy dual subnormality problem for a cyclic analytic $2$-isometry with defect operator of rank two

The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a $2$-isometry is subnormal. In this article, we prove that if $μ$ is a sum of unit point mass measures at two non-antipodal points on the unit circle, then the Cauchy dual $M_z'$ of the multiplication operator $M_z$ on the Dirichlet-type space $D(μ)$ is not subnormal. If the points are antipodal then the subnormality of the said operator has been already established in the literature. Thus, we have a complete solution to CDSP in this case.

math.FA↗

arXiv2025

Joint Complete Monotonicity of reciprocal of a polynomial in two variables

In this article, we study some special cases of the problem of classifying polynomials $p:\mathbb{R}^2_+\to (0,\infty)$ for which the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+}$ is a completely monotone net, where $p(x,y)=b(x)+a(x)y$, $a(x)$ and $b(x)$ are polynomials with $deg(a) < deg (b)$. We also give examples of $a(x)$ and $b(x)$ such that the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+}$ is not completely monotone. Furthermore, we also study some properties of the associated subnormal weighted $2$-shifts.

math.FA↗