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Operator algebras associated with resurgent transforms and differential equations on manifolds with singularities. (English) Zbl 0941.47057
Demuth, Michael (ed.) et al., Spectral theory, microlocal analysis, singular manifolds. Berlin: Akademie Verlag. Math. Top. 14, 300-333 (1997).
A description of the abstract theory of resurgent transforms and their deformations in Banach space together with the associated general operator algebras is given. In the sequel spaces with asymptotics are studied. The Fredholm property for equations on manifolds with cuspidal points of arbitrary order is established. An investigation of the deformation of operators enables the authors to reduce the problem of calculating the indices for manifolds with cuspidal singularities to that on manifolds with conical points.
For the entire collection see [Zbl 0882.00015].
MSC:
47L10 Algebras of operators on Banach spaces and other topological linear spaces
44A15 Special integral transforms (Legendre, Hilbert, etc.)
58J40 Pseudodifferential and Fourier integral operators on manifolds
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