arXiv subjects

Kanha Behera

Publications and source records attributed to Kanha Behera.

2 recordsLinked to original sources

arXiv2025

Multiplicative operators on analytic function spaces

H. J. Schwartz proved in his thesis (1969) that a nonzero bounded operator on Hardy spaces $(H^p, 1\leq p\leq\infty)$ is almost multiplicative if and only if it is a composition operator. But, his proof has a gap. In this article, we show that his result is not correct for $H^\infty$ and we fill the gap for $H^p, 1\leq p<\infty.$ Further, we prove that on several classical spaces such as the Bloch space, the little Bloch space, Besov spaces $B_p$ for $p>1$, and weighted Bergman spaces an operator is almost multiplicative if and only if it is a composition operator. Finally, we give a complete characterization of those composition operators that are multiplicative with respect to the Duhamel product of analytic functions.

math.FA↗

arXiv2025

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 $ψ\in H^\infty$, we show that every automorphism of $ψH^\infty$ must be a composition operator and characterize all such composition operators. Using this characterization, we find all automorphism of $ψH^\infty$ for few choices of $ψ$ with various nature depending on its zeros.

math.CV↗