Tokyo Journal of Mathematics
- Tokyo J. Math.
- Volume 36, Number 1 (2013), 25-47.
Optimal Regularization Processes on Complete Riemannian Manifolds
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 $M$.
Tokyo J. Math., Volume 36, Number 1 (2013), 25-47.
First available in Project Euclid: 22 July 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.tjm/1374497511