相关论文: The Schrodinger-HJW Theorem

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

We revisit one of Zilber's early results in model-theoretic algebra, viz. definability in Schur's lemma. This takes place in a broader context than the original version from the seventies. The present exposition contains results extracted…

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

The paper contains a new proof of the theorem by Krieger which establishes the canonicity of the future cover of a sofic shift. In addition the paper describes a method to produce new canonical covers from a given one, resulting in…

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…

Since a few years, the Schr\"odinger problem captures the attention of a growing community of mathematicians interested in optimal transport problems. The first result of existence of a solution to this problem dates back to 1940, when…

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

The work of Adler provides necessary and sufficient conditions for the Wronskian of a given sequence of eigenfunctions of Schr\"odinger's equation to have constant sign in its domain of definition. We extend this result by giving explicit…

A simple new proof of the Harish-Chandra condition, preceded by an expository part on Hermitian symmetric spaces, holomorphic induction, and on some analytic tools.

This note is a short introduction to the Julia-Wolff-Carath\'eodory theorem, and its generalizations in several complex variables, up to very recent results for infinitesimal generators of semigroups.

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.

We obtain some results related to Romanoff's theorem.

Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators

Rejoinder: Classifier Technology and the Illusion of Progress [math.ST/0606441]