2018/04/15 by Guglielmo Fucci
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Asymptotic analysis #Asymptotic expansion #Diagonal #Geometry #Heat kernel #Kernel (algebra) #Laplace operator #Laplace transform #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Polynomial #Polynomial expansion #Pure mathematics #Spectral Theory in Mathematical Physics #TRACE (psycholinguistics) #math-ph #math.MP
paper · pdf · doi:10.1007/s11005-018-1086-8
published as Lett. Math. Phys. 108, 2453 (2018) · 24 Pages, Latex. To appear in Letters in Mathematical Physics
arxiv created 2018/04/15 · openalex publication_date 2018/04/21 · openalex created_date 2018/04/24 · arxiv updated 2018/10/11 · openalex updated_date 2026/08/05
It is well-known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemmanian manifolds can be obtained through termwise integration of the asymptotic expansion of the on-diagonal heat kernel. It is the purpose of this work to show that, in certain circumstances, termwise integration can be used to obtain the asymptotic expansion of the heat kernel trace for Laplace operators endowed with a suitable polynomial potential on unbounded domains. This is achieved by utilizing a resummed form of the asymptotic expansion of the on-diagonal heat kernel.