Geometrical embeddings for distributions into algebras of generalized functions

2007/09/13 by Shantanu Dave, Dave, Shantanu
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #math.AP

paper · pdf · doi:10.48550/arxiv.0709.2039

arxiv created 2007/09/13 · openalex publication_date 2007/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the distributions.

Related

• A global theory of algebras of generalized functions
• Nonlinear generalised functions on manifolds
• Foundations of a nonlinear distributional geometry
• A Note on Distribution Spaces on Manifolds
• Sheaves of nonlinear generalized function spaces