2014/01/07 by Stephen Clark, Fritz Gesztesy, Clark, Stephen +3
Mathematics · Physics and Astronomy · #34B24 #34C10 #34L05 #34L40 #47A10 #47E05 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Primary 34B20 #Secondary 34B27 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.CA #math.MP #math.SP #msc:34B20 #msc:34B24 #msc:34B27 #msc:34C10 #msc:34L05 #msc:34L40 #msc:47A10 #msc:47E05
paper · pdf · doi:10.48550/arxiv.1401.1285
27 pages, expanded Sect. 2, added references
openalex publication_date 2014/01/07 · arxiv created 2015/06/18 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main objective of this paper is to identify principal solutions associated with Sturm-Liouville operators on arbitrary open intervals (a,b) ⊆ ℝ, as introduced by Leighton and Morse in the scalar context in 1936 and by Hartman in the matrix-valued situation in 1957, with Weyl-Titchmarsh solutions, as long as the underlying Sturm-Liouville differential expression is nonoscillatory (resp., disconjugate or bounded from below near an endpoint) and in the limit point case at the endpoint in question. In addition, we derive an explicit formula for Weyl-Titchmarsh functions in this case (the latter appears to be new in the matrix-valued context).