Related papers: On the Cotlar-Stein lemma

In the paper titled "Bockstein basis and resolution theorems in extension theory" (arXiv:0907.0491v2), we stated a theorem that we claimed to be a generalization of the Edwards-Walsh resolution theorem. The goal of this note is to show that…

The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product…

We calculate the constant term of Coleman power series and use it to prove an analogue of Iwasawa Main Conjecture in function fields of characteristic p>0 using Euler systems. This result is proved by a similar method of classical proof of…

We will present a novel elementary, self-contained, and explicit proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on…

We deduce the existence of a maximal irreducibility measure for a Markov chain from Zorn's lemma.

We prove a no-triplets theorem for spin 1 particles, which implies a strengthened form of the no-cloning theorem.

We prove an iteration theorem which guarantees for a wide class of nice iterations of $\omega_1$-preserving forcings that $\omega_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a…

In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.

A proof of the Riemann hypothesis using the reflection principle is presented.

Zorn's Lemma is a well-known equivalent of the Axiom of Choice. It is usually regarded as a topic in axiomatic set theory, and its historically standard proof (from the Axiom of Choice) relies on transfinite recursion, a non-elementary…

We show that powersets over structures with a bounded counting sequence can be sampled efficiently without evaluating the generating function. An algorithm is provided, implemented, and tested. Runtimes are comparable to existing Boltzmann…

We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…

Working in point-free topology under the constraints of geometric logic, we prove the Fundamental Theorem of Calculus, and apply it to prove the usual rules for the derivatives of $x^\alpha$, $\gamma^x$, and $\log_\gamma x$.

We prove the Lukacs-Olkin-Rubin theorem without invariance of the distribution of the "quotient", which was the key assumption in the original proof of [Olkin--Rubin, Ann. Math. Stat. 33 (1962), 1272--1280]. Instead we assume existence of…

We prove the sufficient conditions for convergence of a certain iterative process of order 2 for solving nonlinear functional equations, which does not require inverting the derivative. We translate and detail our results for a system of…

We illustrate a novel version of Willems' lemma for data-based representation of continuous-time systems. The main novelties compared to previous works are two. First, the proposed framework relies only on measured input-output trajectories…

It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…

It is shown that contrary to claims of Ref. [1] the formulated in the proper physical variables Low theorem [2] for soft photon emission does not require any modification. We also reject the criticism in Ref. [1] of the papers [3,4]. At the…

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in…