Spectral Approximation and Index for Convolution Type Operators on Cones on L^{p}(\mathbb {R}^2) |
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Authors: | H Mascarenhas B Silbermann |
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Institution: | 1. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal 2. Fakult?t für Mathematik, Technische Universit?t Chemnitz, D-09107, Chemnitz, Germany
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Abstract: | We consider an algebra of operator sequences containing, among others, the approximation sequences to convolution type operators
on cones acting on
Lp(\mathbb R2)L^{p}(\mathbb {R}^2), with 1 < p < ∞. To each operator sequence (An) we associate a family of operators
Wx(An) ? L(Lp(\mathbb R2))W_{x}(A_{n}) \in \mathcal {L}(L^{p}(\mathbb {R}^2)) parametrized by x in some index set. When all Wx(An) are Fredholm, the so-called approximation numbers of An have the α-splitting property with α being the sum of the kernel dimensions of Wx(An). Moreover, the sum of the indices of Wx(An) is zero. We also show that the index of some composed convolution-like operators is zero. Results on the convergence of
the e\epsilon-pseudospectrum, norms of inverses and condition numbers are also obtained. |
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Keywords: | |
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