On traces and modified Fredholm determinants for half-line Schr "odinger\n operators with purely discrete spectra

2018/04/18 by Fritz Gesztesy, Klaus Kirsten, Gesztesy, Fritz +1 · 1 citation
Mathematics · Physics and Astronomy · #34L40 #47B10 #47G10. Secondary: 34B27 #FOS: Mathematics #Numerical methods in inverse problems #Primary: 47A10 #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1804.06887

openalex publication_date 2018/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After recalling a fundamental identity relating traces and modified Fredholm\ndeterminants, we apply it to a class of half-line Schr "odinger operators (-\nd²/dx²) + q on (0,\∞) with purely discrete spectra. Roughly speaking,\nthe class considered is generated by potentials q that, for some fixed C₀ >\n0, \ε > 0, x₀ \∈ (0, \∞), diverge at infinity in the manner\nthat q(x) \≥ C₀ x^{(2/3) + \ε₀} for all x \≥ x₀. We treat\nall self-adjoint boundary conditions at the left endpoint 0.\n

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