2021/11/07 by Jan Dereziński, Dereziński, Jan, Jérémy Faupin +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Bessel function #Chemistry #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic function #Integrable system #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Operator (biology) #Operator theory #Physics #Pure mathematics #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP
paper · pdf · doi:10.48550/arxiv.2111.04109
published in arXiv (Cornell University) (Cornell University) · 67 pages
openalex publication_date 2021/11/07 · arxiv created 2022/02/03 · arxiv updated 2022/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study perturbed Bessel operators Lm2=- ∂2x + ( m2 - \frac14 )(1)/(x2) + Q(x) on L2]0,∞[, where m∈ℂ and Q is a complex locally integrable potential. Assuming that Q is integrable near ∞ and x↦ x1-εQ(x) is integrable near 0, with ε≥0, we construct solutions to Lm2 f = - k2 f with prescribed behaviors near 0. The special cases m=0 and k=0 are included in our analysis. Our proof relies on mapping properties of various Green's operators of the unperturbed Bessel operator. Then we determine all closed realizations of Lm2 and show that they can be organized as holomorphic families of closed operators.