arXiv subjects

Bhupendra Paudyal

Publications and source records attributed to Bhupendra Paudyal.

3 recordsLinked to original sources

arXiv2018

The lattices of invariant subspaces of a class of operators on the Hardy space

In the authors' first paper, Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra operator. Current work is an extension of the previous work and it describes the lattice of invariant subspaces of the shift plus a positive integer multiple of the complex Volterra operator on the Hardy space. Our work was motivated by a paper by Ong who studied the real version of the same operator.

math.CV↗

arXiv2017

Eigenfunctions of Composition Operators on Bloch-type Spaces

Suppose $φ$ is a holomorphic self map of the unit disk and $C_φ$ is a composition operator with symbol $φ$ that fixes the origin and $0<|φ'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic solutions of Schröder equation for the composition operator $C_φ$ belong to a Bloch-type space $\mathcal{B}_α$ for some $α>0$. The results from composition operators have been extended to weighted composition operators in the second part of this work.

math.CV↗

arXiv2015

Invariant subspaces of the shift plus complex Volterra operator

The lattice of closed invariant subspaces of the Volterra operator acting on $L^2(0,1)$ was completely described by Sarason. On the other hand, he explicitly found the lattice of closed invariant subspaces of the shift plus Volterra operator on $L^2(0,1)$. Inspired by Sarason's results, we find the lattice of closed invariant subspaces of the shift plus complex Volterra operator acting on the Hardy space

math.CV↗