Linear operators. Part II. Spectral theory

By N. Dunford, Jacob T. Schwartz. 2003

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Symplectic hypersurfaces and transversality in Gromov-Witten theory (2007, background): “hat Λ(Dfξ) = 0 for all smooth sections ξ: S 2→ Bwith compact support in S∗ := S \ {z 1,...,zk}. Elliptic regularity for distributions (see [22], Theorem 8.12 for the case with constant coeﬃcients and [6], Chapter XIV, Theorem 6.2., p. 1704 for the general case) implies that the restriction of Λ to S”
Continuous slice functional calculus in quaternionic Hilbert spaces (2012, background): “5 of [10]), there exists an orthogonal decomposition ⊕ l∈ΛHl of H Jı + into closed subspaces and, for every l ∈ Λ, a positive σ–additive Borel measure μl on σ(T+) and an isometric isomorphism Ul from L 2 l := L (2)(σ(T+),C;μl) to Hl such that Hl is invariant under T+ and T ∗ + (and thus under A+ and”
Efficient estimation of general dynamic models with a continuum of moment conditions (2007, background): “8 For a definition and the properties of Hilbert-Schmidt operators, see Dunford and Schwartz (1988).”
On Learning Over-parameterized Neural Networks: A Functional Approximation Prospective (2019, background): “Let λ 1 ≥ λ 2 ≥ . . . be the spectrum of L K deﬁned in (11), whose existence is given by the spectral theorem [DS63, Theorem 4, Chapter X.3].”