Methods of Modern Mathematical Physics. I: Functional Analysis

By M. Reed. 1972

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Citations in the corpus

Learning Theory for Distribution Regression (2014, neutral): “We divide the proof into 3 steps: • k: continuous, bounded ⇒ µ: H-measurable: The mapping µ : (M+1 (X),B(τw)) → (H,B(H)) is measurable, iff the Lh : (M+1 (X),B(τw)) → (R,B(R)) map defined as Lh(x) = 〈h, µx〉H ( = ∫ X h(u)dx(u) ) is measurable for ∀h ∈ H (Reed and Simon, 1980, Theorem IV.”
Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “In order to stably represent the low frequency content of f deﬁned on the vertices of the graph, it is convenient to introduce a second class of waveforms, analogous to the lowpass residual scaling functions from classical wavelet analysis.”
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction (2008, background): “This follows from strong resolvent convergence of H ε N to HN as ε → 0 by Trotter’s theorem [18].”
Local and global smoothing effects for some linear hyperbolic equations with a strong dissipation (2014, unknown): “4 of [28]), there exist a measure space (M,μ) with μ a finite measure, a unitary operator Ψ : H → L(2)(M,μ), and a real valued nonnegative function λ(ξ), defined for almost every ξ ∈ M , such that • u ∈ D(A) if and only if λ(ξ)[Ψ(u)](ξ) ∈ L(2)(M,μ), • [Ψ(Au)](ξ) = λ(ξ)[Ψ(u)](ξ) for almost every ξ ∈ ”
Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control (2005, background): “[ RS80 , p. 203]) there exist an orthonormal basis {ψi}i∈IN for X and a sequence {λi}i∈IN of nonnegative real numbers so that”
Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs (2015, background): “The symbol ⊗ denotes the tensor product of Hilbert spaces [34], as well as the Kronecker product of matrices.”
Von Neumann Algebras (2009, background): “Obviously if σ ∈ Sn, ξσ(1) ∧ ξσ(1) ∧ ξσ(2) · · · ∧ ξσ(n) = (−1)ξ1 ∧ ξ2 ∧ · · · ∧ ξn.”
Perturbed closed geodesics are periodic orbits: Index and transversality (2001, methodology): “According to Baire’s category theorem [ RS80 , section III.5] such a set is dense.”