Spectral properties and self-adjoint extensions of the third power of the radial Laplace operator

2014/10/06 by T. A. Bolokhov, Bolokhov, T. A.
Computer Science · Mathematics · Physics and Astronomy · #47A10 #47B25 (Primary) #81Q10 (Secondary) #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #hep-th #math.SP #msc:47A10 #msc:47B25 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.1410.1487

20 pages

arxiv created 2014/10/06 · openalex publication_date 2014/10/06 · arxiv updated 2014/10/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider self-adjoint extensions of differential operators of the type (-(d²)/(dr²) + (l(l+1))/(r²))³ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and its first derivative and second that nullify the 4th (l=1) or the 3rd (l=2) derivative. We calculate the expressions for the correponding resolvents and derive spectral decompositions. These types of boundary conditions are interesting from the physical point of view, especially the second ones, which give an example of emergence of long-range action in exchange for a singularity at the origin.

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