Boundedness of spectral multipliers of generalized Laplacians on compact\n manifolds with boundary

2014/10/22 by Mayukh Mukherjee, Mukherjee, Mayukh · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1410.6041

openalex publication_date 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a second order, strongly elliptic negative semidefinite differential\noperator L (maybe a system) on a compact Riemannian manifold \M\nwith smooth boundary, where the domain of L is defined by a coercive boundary\ncondition. Classically known results, and also recent work in citeDOS and\n citeDM establish sufficient conditions for L^\∞-\BMO_L\ncontinuity of \φ(\√(A)), where \φ \∈ S⁰₁(\ℝ), and\nA is a suitable elliptic operator. Using a variant of the\nCheeger-Gromov-Taylor functional calculus due to citeMMV, and short time\nbounds on the integral kernel of e^tL due to citeG, we prove that a\nvariant of such sufficient conditions holds for our operator L.\n

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