2001/11/28 by A. Melin, Anders Melin, Melin, A. +3
Computer Science · Mathematics · #31C10 #35P05 #37J45 #37K05 #47J20 #58J52 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #math.FA #math.SP #msc:31C10 #msc:35P05 #msc:37J45 #msc:37K05 #msc:47J20 #msc:58J52
paper · pdf · doi:10.48550/arxiv.math/0111292
arxiv created 2001/11/28 · openalex publication_date 2001/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an h-pseudodifferential operator P, whose symbol extends holomorphically to a tubular neighborhood of the real phase space and converges sufficiently fast to 1, so that the determinant of P is well-defined. We show that the modulus of this determinant is asymptotically bounded by an exponential of the integral of the logarithm of the modulus of the symbol along a certain complex deformation of the real phase space. Since there are many possible such deformations, we get a variational problem. The paper is devoted to the corresponding variational calculus.