Journal of Operator Theory
Volume 85, Issue 1, Winter 2021 pp. 229-256.
Fredholm conditions for invariant
operators: finite abelian groups and boundary value problems
Authors:
Alexandre Baldare (1), Remi Come (2), Matthias Lesch (3), Victor Nistor (4)
Author institution: (1) Universite Lorraine, 57000 Metz,
France
(2) Universite Lorraine, 57000 Metz,
France
(3) Mathematisches
Institut, Univ. Bonn, Endenicher Allee 60, 53115 Bonn,
Germany
(4) Universite Lorraine, 57000 Metz,
France
Summary: Let $\Gamma$ be a finite abelian group acting on a smooth, compact
manifold $M$ without boundary and let $P \in \psi^m(M; E_0, E_1)$ be a
$\Gamma$-invariant, classical, pseudodifferential operator acting
between sections of two $\Gamma$-equivariant vector bundles. Let
$\alpha$ be an irreducible representation of $\Gamma$. We obtain
necessary and sufficient conditions for the restriction $\pi_\alpha(P)
: H^s(M; E_0)_\alpha \to H^{s-m}(M; E_1)_\alpha$ of $P$ between the
$\alpha$-isotypical components of Sobolev spaces to be Fredholm.
DOI: http://dx.doi.org/10.7900/jot.2019feb26.2270
Keywords: Fredholm operator, pseudodifferential operator, finite abelian group, invariant
operator, isotypical component, elliptic theory
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