Trace ideals and their applications

By Barry Simon. 1979

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Citations in the corpus

On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, background): “Since ∫ X k(x, x)dρ(x) is finite, Σ is self-adjoint, positive semi-definite and trace-class (Simon, 1979).”
Cauchy–Schwarz norm inequalities for weak∗-integrals of operator valued functions (2005, background): “6 of [25].”
Cauchy-Binet for Pseudo-Determinants (2013, background): “1) Despite the simplicity of the proof and similar looking results for minor expansion, formulas in multi-linear algebra [27], condensation formulas, trace ideals [40], formulas for the characteristic polynomial [30, 36, 9], pseudo inverses, noncommutative generalizations [39], we are not aware that”
Sum rules for Jacobi matrices and their applications to spectral theory (2001, methodology): “Lemma 2.3. If A is a matrix and �·� p the Schatten Ip norm [ 53 ] ,t hen”
Necessary conditions for Schatten class localization operators (2005, unknown): “The norm on Sp is given by ‖L‖Sp = ‖λ‖p (see the standard references [18, 17]).”
Lectures on integrable probability (2012, unknown): “[Lax-02] or [Simon-05]) for det(1−KAiry(x, y))L2(s,+∞).”
Existence of minimizers for Kohn-Sham models in quantum chemistry (2009, background): “For all W ∈ C∞ c (R3), the operator (1 + |∇|)−1W(1 + |∇|)−1 is compact (it is even in the Schatten class Sp for all p > (3)2 in virtue of the Kato–Seiler–Simon inequality [29]), yielding ∫”
Detecting Confounding in Multivariate Linear Models via Spectral Analysis (2017, background): “(33) Proof: (33) is a special case of the so-called Aronszajin-Krein formula [21, 22, 23, 24, 25].”
Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties (2003, methodology): “Here we used Berezin’s inequality [20]: if K is a self-adjoint operator and P is a projection operator on a Hilbert space, then tr ( Pφ(K)P )≥ tr(φ(PKP )) (4.”
Orthogonal polynomials on the unit circle: New results (2004, background): “Indeed, if d = dist(z 0 , Γ), δ ≥ d 2 /2 and so, Theorem 4.3 says that there is at most one zero in the circle of radius d 2 /6.”
Universality for eigenvalue correlations from the modified Jacobi unitary ensemble (2002, background): “20 of [24] and the positivity of Dn,s and Jα,s, it then suffices to prove that Dn,s → Jα,s weakly, and that trDn,s → tr Jα,s as n→ ∞.”
On the Strichartz estimates for orthonormal systems of initial data with regularity (2017, background): “For details about the Schatten classes the reader may consult the book by Simon [33].”
Curve Forecasting by Functional Autoregression (2008, unknown): “6 in [23], we can estimate this as follows: μk+1 ( ẑΓ̂ α )”
Brownian Gibbs property for Airy line ensembles (2011, methodology): “The point process given by D̃N(N,A) may be written in terms of a correlation kernel KN ; as N goes to infinity, this kernel converges in the traceclass norm (see [72] for a definition) to a limiting kernel, known as the Airy kernel KAi.”