2015/11/05 by A. Yu. Savin, Anton Savin, B. Yu. Sternin +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Conical surface #Elliptic operator #Fredholm operator #Gravitational singularity #Holomorphic and Operator Theory #Manifold (fluid mechanics) #Operator (biology) #Principal part #Property (philosophy) #Spectral Theory in Mathematical Physics #Symbol (formal) #math.AP #math.OA #msc:35J70 #msc:46L89 #msc:58J20
paper · pdf · doi:10.1007/s10958-018-3973-z
published as J. Math. Sci., V. 233, N. 6, 2018, 930-948 · 24 pages, 5 figures
arxiv created 2015/11/05 · openalex created_date 2016/06/24 · openalex publication_date 2018/08/04 · arxiv updated 2020/08/04 · openalex updated_date 2026/08/06
In the present work we study elliptic operators on manifolds with singularities in the situation, when the manifold is endowed with an action of a discrete group G. As usual in elliptic theory, the Fredholm property of an operator is governed by the properties of its principal symbol. We show that the principal symbol in our situation is a pair, consisting of the symbol on the main stratum (interior symbol) and the symbol at the conical point (conormal symbol). Fredholm property of elliptic elements is obtained.