2019/01/08 by Pham Viet Hai, Hai, Pham Viet
Mathematics · #47 B38 #47 E99 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:47 #msc:B38 #msc:E99
paper · pdf · doi:10.48550/arxiv.1901.02331
14 pages
arxiv created 2020/02/28 · arxiv updated 2020/03/02
Given holomorphic functions ψ0 and ψ1, we consider first-order differential operators acting on Hardy space, generated by the formal differential expression E(ψ0,ψ1)f(z)=ψ0(z)f(z)+ψ1(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.