Spectral approximation of linear operators

By F. Chatelin. 2011

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Nonparametric stochastic discount factor decomposition (2014, background): “ollows some arguments from the proof of Proposition 4.2 of Gobet et al. (2004). Take KK and let P K = (˚ K ˚ K ) denote the spectral projection of KM corresponding to ˆ K. By Lemma 6.4 on p. 279 of Chatelin (1983), we have that ˚ P K˚ 1 2ˇi Z R( KM;z) ˆ z dz ( KM M)˚ and so k˚ P K˚k 1 2ˇ Z R( KM”
Properties of design-based functional principal components analysis (2008, background): “Going back to criterion (2), one can express it as follows Rq(φ1, φ2, . . . , φq) = 1 N ∑ k∈U ‖Yk − µ‖2 − q∑ j=1 〈Γφj , φj〉 (5) and we get by maximal properties of the eigenvalues (see Chatelin, 1983) that the minimum of Rq(φ1, φ2, . . . , φq) is attained for φ1 = v1, . . . , φq = vq.”
Morley Finite Element Method for the Eigenvalues of the Biharmonic Operator (2014, background): “Let It is well known from the spectral theory of selfadjoint compact operators [18, 30] that the eigenvalue problem (3.1) has countably many eigenvalues, which are real and positive with + ∞ as only possible accumulation point.”
A parametric estimation method for dynamic factor models of large dimensions (2009, neutral): “By Theorems 5.6 and 5.8 of Chatelin (1983) g(Æ) is bounded, continuous and differentiable, and therefore admits a first-order Taylor expansion.”