Ellipticity of the quantum mechanical Hamiltonians: corner singularity of the helium atom

Asymptotic parametrices of elliptic edge operators

“…Concrete results on the index of elliptic edge symbols may be found in [10]. Bijectivity results are also announced in [7]. Another useful observation is that there are always so-called smoothing Mellin plus Green symbols σ 1 (M + G)(y, η) of the edge calculus such that σ 1 (A + M + G)(y, η) is bijective.…”

“…The recent experience of the authors with the problem of explictly computing the asymptotic data of solutions, cf. the articles [6], [7], is that it needs parallel work to organise the construction of parametrices and of the underlying symbolic structures in a more transparent and accessible way. Of course, we refer to the basics of the cone and edge calculus, known from a number of articles and monographs, cf.…”