Tokyo Journal of Mathematics

Optimal Regularization Processes on Complete Riemannian Manifolds

Shantanu DAVE, Günther HÖRMANN, and Michael KUNZINGER

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Abstract

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 $M$.

Article information

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

Dates
First available in Project Euclid: 22 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1374497511

Digital Object Identifier
doi:10.3836/tjm/1374497511

Mathematical Reviews number (MathSciNet)
MR3112375

Zentralblatt MATH identifier
1283.46049

Subjects
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

Citation

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. https://projecteuclid.org/euclid.tjm/1374497511


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