A DENSE SUBSET OF THE OPERATOR DOMAIN
WITH A POINT INTERACTION

Hector J. Cabarcas U. $^1$, Arbey Araujo $^1$,
Ruben D. Ortiz O. $^{1,\S}$

$^1$ Waves Research Group
Department of Mathematics
Universidad de Cartagena
Cartagena de Indias - 130001, COLOMBIA

Abstract


Abstract. In this paper, we investigate the domain of the operator with a point interaction, specifically the operator $-\frac{d^2}{dx^2}+Z\delta_0$. We demonstrate the existence of a dense subset within this domain consisting of functions that possess compact support and are smooth everywhere except, possibly, at $x = 0$. Our findings shed light on the structural properties of the operator domain, providing valuable insights into its mathematical characterization and potential applications.

Received: 14 July 2023

AMS Subject Classification: 81V05, 47A30, 40A10

Key Words and Phrases: point interaction; dense subspace; dominated convergence theorem; regularization

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How to cite this paper?
DOI: 10.12732/ijam.v36i6.3
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2023
Volume: 36
Issue: 6
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