Complex symmetry of first-order differential operators on Hardy space

Pham Viet Hai

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arXiv · 1901.02331

Complex symmetry of first-order differential operators on Hardy space

Pham Viet Hai

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Abstract

Given holomorphic functions $ψ_0$ and $ψ_1$, we consider first-order differential operators acting on Hardy space, generated by the formal differential expression $E(ψ_0,ψ_1)f(z)=ψ_0(z)f(z)+ψ_1(z)f'(z)$. We characterize these operators which are complex symmetric with respect to weighted composition conjugations. In parallel, as a basis of comparison, a characterization for differential operators which are hermitian is carried out. Especially, it is shown that hermitian differential operators are contained properly in the class of $\calC$-selfadjoint differential operators. The calculation of the point spectrum of some of these operators is performed in detail.

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BibTeX RIS

Pham Viet Hai. 2020-02-28. Complex symmetry of first-order differential operators on Hardy space. https://arxiv.org/abs/1901.02331

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