2008/01/17 by Jamil Abed, Abed, Jamil, Bert‐Wolfgang Schulze +2
Computer Science · Mathematics · #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.AP #msc:35J70
paper · pdf · doi:10.48550/arxiv.0801.2636
40 pages
openalex publication_date 2008/01/17 · arxiv created 2008/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near a corner point.