The Damped String Problem Revisited

2010/09/09 by Fritz Gesztesy, Helge Holden, Gesztesy, Fritz +1 · 1 citation
Mathematics · Physics and Astronomy · #35J40 #47A05 #47F05 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 35J25 #Secondary 47A10 #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35J25 #msc:35J40 #msc:47A05 #msc:47A10 #msc:47F05

paper · pdf · doi:10.48550/arxiv.1009.1858

39 pages

arxiv created 2010/09/09 · arxiv updated 2010/09/10

Abstract

We revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it, employing methods familiar from supersymmetric quantum mechanics. We also derive completeness and Riesz basis results (with parentheses) for the associated root functions under less smoothness assumptions on the coefficients than usual, using operator theoretic methods (rather than detailed eigenvalue and root function asymptotics) only.

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