منابع مشابه
Positivity and Conditional Positivity of Loewner Matrices
We give elementary proofs of the fact that the Loewner matrices [ f(pi)−f(pj) pi−pj ] corresponding to the function f(t) = t on (0,∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0,∞) the Loewner matrices corresponding to an operator convex function on...
متن کاملPositivity And
We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An alternative proof of this result is provided. We also give an intriguing log-concavity property of Schur functions. 1. Schur positivity conjectures The ring of...
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The state-dependent delay differential equation ẋ(t)+ m ∑ i=1 pi(t)x ( t − (Hix)(t) )= f (t), t ∈ [0,∞), x(ξ)= φ(ξ), ξ < 0, with state-dependent impulses is under consideration. Sufficient conditions for positivity of solutions to the Cauchy and periodic problems as well as conditions for positivity of solutions to the problem with a condition on the right end of the interval [0,ω] are given. S...
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We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality CD ≤ CN between Dirichlet and Neumann covariance operators on a manifold with a reflection.
متن کاملPositivity and Integrability
Based on past contributions by Robert Schrader and Michael Karowski I review the problem of existence of interacting quantum field theory and present recent ideas and results on rigorous constructions. 1 Historical remarks The title of this essay is identical to that of a small conference at the FU-Berlin in honor of Michael Karowski and Robert Schrader at the occasion of their sixtyfifth birth...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2000
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6882