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Anisotropic Edge Pseudo — Differential Operators with Discrete Asymptotics
Author(s) -
Buchholz Thilo
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19971840104
Subject(s) - mathematics , differential calculus , manifold (fluid mechanics) , differential operator , differential (mechanical device) , gravitational singularity , mathematical analysis , quantum differential calculus , differential equation , vector calculus , anisotropy , calculus (dental) , pure mathematics , mechanical engineering , medicine , physics , dentistry , quantum mechanics , noncommutative quantum field theory , engineering , noncommutative geometry , aerospace engineering
An anisotropic pseudo — differential calculus aimed at solving parabolic differential and pseudo — differential equations in terms of Volterra pseudo–differential operators was studied by Piriou for spatial variables on a closed C ∞– manifold. Such a program also makes sense when the spatial variables run over a manifold with edges. Our approach deals with this case. It covers, in particular, manifolds with conical singularities. The main point of the present paper is the anisotropic edge pseudo — differential calculus, obtained as a substructure of our corresponding abstract anisotropic edge calculus with operator — valued symbols.