arXiv subjects

Milan Kumar Mal

Publications and source records attributed to Milan Kumar Mal.

5 recordsLinked to original sources

arXiv2026

The Subnormality of $\mathbb K$-Homogeneous Multiplication Operators on Bounded Symmetric Domains

Let $Ω=G/\mathbb K$ be an irreducible bounded symmetric domain of rank $r$ and dimension $d.$ In this paper, we study the joint subnormality of $d$-tuple of multiplication operators induced by the coordinate functions on reproducing kernel Hilbert spaces of holomorphic functions on $Ω$ determined by $\mathbb K$-invariant kernels. We introduce the notion of contractive $d$-tuple associated with $Ω$ and prove that the weighted Bergman shifts on $Ω$ are contractive $d$-tuple precisely when they are jointly subnormal. A characterization of joint subnormality further leads to the study of a class of moment problems, which we refer to as twisted moment problems. We establish that the twisted moment problem is equivalent to an appropriate Hausdorff moment problem. This equivalence provides a moment-theoretic characterization of joint subnormality for the multiplication operators under consideration.

math.FA↗

arXiv2026

Commutant lifting and interpolation on quotients of bounded symmetric domains

Let $Ω\subseteq \mathbb C^d$ be a bounded symmetric domain, $G$ a finite complex reflection group acting on $\mathbb C^d$, and $\boldsymbol θ:Ω\to \boldsymbol θ(Ω)$ the associated proper holomorphic map factored by $G.$ In this paper, we investigate commutant lifting and interpolation by Schur functions on the quotient domain $\boldsymbol θ(Ω).$ For a given quotient module of the Hardy space $H^2(\boldsymbolθ(Ω))$, we obtain equivalent criteria for a contractive module map to admit a Schur-class lift: one in terms of the contractivity of an associated functional on a subspace of $L^1(\partial\boldsymbolθ(Ω))$, and another in terms of a geometric distance formula in the same $L^1$-space. Specializing to quotient domains of the polydisc factored by imprimitive finite complex reflection groups, we obtain a commutant lifting criterion formulated in terms of inner functions. Finally, we apply these operator-theoretic results to finite-point Nevanlinna-Pick type interpolation problems on $\boldsymbol θ(Ω)$. Since the symmetrized bidisc and the tetrablock arise as quotient domains of suitable bounded symmetric domains, these criteria apply in particular to those domains.

math.FA↗

arXiv2025

Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem

We introduce a Schur-Agler type class associated with the tetrablock and establish a realization theorem for this class. Furthermore, we provide a tetrablock analog of the interpolation theorem, extension theorem, and the Toeplitz corona theorem.

math.FA↗

arXiv2025

Brown-Halmos type characterization for the tetrablock

In this note, we obtain a Brown-Halmos type characterization for Toeplitz operators on the Hardy space associated with the tetrablock. As an application, we show that the zero operator is the only compact Toeplitz operator.

math.FA↗

arXiv2025

Cartan Isometries and Toeplitz Operators on Cartan domains

We provide a description of the Shilov boundary of the classical Cartan domain in terms of Jordan triple determinant. As a consequence, we obtained an intrinsic characterization of Cartan isometries. Further, we obtain (i) invariance of Cartan isometries under the action of the biholomorphic automorphism group, and (ii) a Brown-Halmos type condition for Toeplitz operators on the Cartan domain. Also, we show that the zero operator is the only compact Toeplitz operator. Finally, we study the $\boldsymbol T$-Toeplitz operators and reflexivity of a Cartan isometry $\boldsymbol T.$

math.FA↗