The inverse approach to Dirac-type systems based on the A-function\n concept

2019/03/02 by Fritz Gesztesy, Gesztesy, Fritz, Alexander Sakhnovich +1
Mathematics · Physics and Astronomy · #34B20 #34L40 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Primary 34A55 #Quantum Mechanics and Non-Hermitian Physics #Secondary 34B24 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1903.00779

openalex publication_date 2019/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The principal objective in this paper is a new inverse approach to general\nDirac-type systems modeled after B. Simon's 1999 inverse approach to half-line\nSchr "odinger operators. In particular, we derive the so-called A-equation\nassociated to Dirac-type systems and, given a fundamental positivity condition,\nwe prove that this integro-differential equation for A is uniquely solvable. We\nshow how to recover the matrix-valued potential coefficient from A. This\napproach is also applicable to matrix-valued Schr "odinger operators on a\nhalf-line.\n

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