Related papers: On the Cotlar-Stein lemma
In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.
A new proof for a newly proved conjecture of Soltani and Roozegar (2012) is provided; our proof does not make any use of the Stieltjes transform unlike the proof of Roozegar and Soltani (2013), and the distribution of power semicircle has…
The rank of tensors is not additive with respect to the direct sum.
We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.
We give a short proof of the most general version of the Nullstellensatz without using the Axiom of Choice.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
We settle in the affirmative the Graham-Sloane conjecture.
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and…
We observe that justification logic enjoys a form the strong finite model property (sometimes also called small model property). Thus we obtain decidability proofs for justification logic that do not rely on Post's theorem.
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
We describe a formal proof of the independence of the continuum hypothesis ($\mathsf{CH}$) in the Lean theorem prover. We use Boolean-valued models to give forcing arguments for both directions, using Cohen forcing for the consistency of…
This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.
The recent non-calculus proof of Kepler's first law succeeds because of an obscure, but valid property of the ellipse.
Although it is easy to prove the sufficient conditions for optimality of a linear program, the necessary conditions pose a pedagogical challenge. A widespread practice in deriving the necessary conditions is to invoke Farkas' lemma, but…
We extend Stein's lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein's lemma, with the first being a rigorous proof by mathematical induction. The…
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We add a few ideas to Erd\H{o}s's proof of Bertrand's Postulate to produce one using a little calculus but requiring direct check only for $n\leq 5$ and one without using calculus and requiring direct check only for $n\leq 12$. The proofs…
We supply the first proof of Krein's Trace Theorem which does not use complex analysis. Our proof holds for~$\sigma$-finite von Neumann algebras $\mathcal{M}$ of type II and unbounded perturbations from the predual of~$\mathcal{M}$.
The pumping lemma and Ogden lemma offer a powerful method to prove that a particular language is not context-free. In 2008 Kanazawa proved an analogue of pumping lemma for well-nested multiple-context free languages. However, the statement…