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On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

100%

Sternin B.

Open Mathematics

2011

tom 9

nr 4

814-832

We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.

Asymptotic solutions to Fuchsian equations in several variables

63%

Sternin B., Shatalov V.

Banach Center Publications

1996

tom 33

nr 1

351-363

The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Sternin B.

1 Shatalov V.

1 2011

1 1996

Wyniki wyszukiwania

On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

Asymptotic solutions to Fuchsian equations in several variables