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We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. 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 involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.
Aspects of Boundary Problems in Analysis and Geometry : advances in partial differential equations
(2004)
General Relativity and Gravitation is a journal of studies in general relativity and related topics, published under the auspices of the International Committee on General Relativity and Gravitation. The journal publishes original, high-quality research papers on the theoretical and experimental aspects of general relativity and related topics; surveys and review articles on current research in general relativity and gravitation; news regarding conferences and other enterprises of interest to scientists in this field; and book reviews. All manuscripts and editorial correspondence, as well as books for review, should be submitted to the Editor, and authors may propose who among the Associate Editors will deal with their paper. All submitted articles are acknowledged and refereed.