arXiv subjects

Deepak K. Pradhan

Publications and source records attributed to Deepak K. Pradhan.

2 recordsLinked to original sources

arXiv2025

Inner and characteristic functions in polydiscs

Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a suitable domain and make significant contributions to the development of various theories in Hilbert function spaces. In this paper, we solve this problem in polydiscs. In particular, we present a concrete description of the characteristic functions of tuples of commuting pure contractions and, consequently, provide a description of inner functions on polydiscs.

math.FA↗

arXiv2023

Pairs of inner projections and two applications

Orthogonal projections onto closed subspaces of $H^2(\mathbb{D}^n)$ of the form $φH^2(\mathbb{D}^n)$ for inner functions $φ$ on $\mathbb{D}^n$ are referred to as inner projections, where $H^2(\mathbb{D}^n)$ denotes the Hardy space over the open unit polydisc $\mathbb{D}^n$. In this paper, we classify pairs of commuting inner projections. We also present two seemingly independent applications: the first is an answer to a question posed by R. G. Douglas, and the second is a complete classification of partially isometric truncated Toeplitz operators with inner symbols on the polydisc.

math.FA↗