Tokyo Journal of Mathematics

Optimal Regularization Processes on Complete Riemannian Manifolds

Shantanu DAVE, Günther HÖRMANN, and Michael KUNZINGER

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We study regularizations of Schwartz distributions on a complete Riemannian manifold $M$. These approximations are based on families of smoothing operators obtained from the solution operator to the wave equation on $M$ derived from the metric Laplacian. The resulting global regularization processes are optimal in the sense that they preserve the microlocal structure of distributions, commute with isometries and provide sheaf embeddings into algebras of generalized functions on $M$.

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Tokyo J. Math., Volume 36, Number 1 (2013), 25-47.

First available in Project Euclid: 22 July 2013

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Zentralblatt MATH identifier

Primary: 58J37: Perturbations; asymptotics
Secondary: 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 46T30: Distributions and generalized functions on nonlinear spaces [See also 46Fxx] 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15] 35L05: Wave equation


DAVE, Shantanu; HÖRMANN, Günther; KUNZINGER, Michael. Optimal Regularization Processes on Complete Riemannian Manifolds. Tokyo J. Math. 36 (2013), no. 1, 25--47. doi:10.3836/tjm/1374497511.

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