arXiv subjects

Rahul Maurya

Publications and source records attributed to Rahul Maurya.

3 recordsLinked to original sources

arXiv2026

Generalized tri-circular projections on some spaces of analytic functions

In this paper, we obtain the structure of a class of contractive projections, known as generalized tri-circular projections, on some functional Banach spaces on the open unit disk $\mathbb{D}$, which includes Hardy, Bergman and Bloch spaces. We then consider the space $S^p_{\mathcal{K}}$ of $\mathcal{K}$-valued analytic functions on $\mathbb{D}$ such that $f' \in H^p(\mathcal{K})$ and give complete description of generalized tri-circular projections on this space. Here, $\mathcal{K}$ is a complex separable Hilbert space, and $H^p(\mathcal{K})$ denotes the Hardy space of $\mathcal{K}$-valued analytic functions on $\mathbb{D}$.

math.FA↗

arXiv2024

Automorphisms of subalgebras of bounded analytic functions

Let $H^\infty$ denote the algebra of all bounded analytic functions on the unit disk. It is well-known that every (algebra) automorphism of $H^\infty$ is a composition operator induced by disc automorphism. Maurya et al., (J. Math. Anal. Appl. 530 : Paper No: 127698, 2024) proved that every automorphism of the subalgebras $\{f\in H^\infty : f(0) = 0\}$ or $\{f\in H^\infty : f'(0) = 0\}$ is a composition operator induced by a rotation. In this article, we give very simple proof of their results. As an interesting generalization, for any $\psi\in H^\infty$, we show that every automorphism of $\psi H^\infty$ must be a composition operator and characterize all such composition operators. Using this characterization, we find all automorphism of $\psi H^\infty$ for few choices of $\psi$ with various nature depending on its zeros.

math.CV↗

arXiv2023

Automorphisms and generalized projections on spaces of analytic functions

We present complete classifications of automorphisms of two closed subalgebras of the bounded analytic functions on the open unit disc $\mathbb{D}$, namely, the subalgebra of functions vanishing at the origin, and the subalgebra of functions whose first derivative vanishes at the origin. The later subalgebra is known as the Neil algebra. We also characterize generalized tri-circular projections on $H^{p}(\mathbb{D})$ and $H^{p}(\mathbb{D}^2)$, $1\leq p \leq \infty$, $p\neq 2$.

math.CV↗