A note on uniqueness of extension for characteristic functions

Existence and uniqueness properties for solutions of a class of Banach space valued evolution equations

In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The framework of our abstract result includes, for example, finite dimensional ordinary differential equations (ODEs), semilinear deterministic partial differential equations (PDEs), as well as certain additive noise driven stochastic partial differential equations (SPDEs) as special cases. The framework of our general result assumes somehow mild regularity conditions on the involved semigroup and also allows the involved sem…

A note on an extension of Gelfond's constant

The aim of this note is to provide a natural extension of Gelfond's constant $e^π$ using a hypergeometric function approach. An extension is also found for the square root of this constant. A few interesting special cases are presented.

Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres.

On uniqueness of the Laplace transform on time scales

After introducing the concept of null functions, we shall present a uniqueness result in the sense of the null functions for the Laplace transform on time scales with arbitrary graininess. The result can be regarded as a dynamic extension of the well-known Lerch's theorem.

A note on the well posed anisotropic discrete BVP's

Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.

Poincaré type inequality for Dirichlet spaces and application to the uniqueness set

We give an extension of Poincaré's type capacitary inequality for Dirichlet spaces and provide an application to study the uniqueness sets on the unit circle for these spaces.

A note on some applications of the extension of Abel's lemma

We offer some new applications of an extension of Abel's lemma, as well as its more general form established by Andrews and Freitas. A nice connection is established between this lemma and series involving the Riemann zeta function.

关于Norton-Sullivan拟共形扩展的唯一性

On the Uniqueness of the Norton-Sullivan Quasiconformal extension

该研究证明了Norton-Sullivan扩展映射是将实数上的bi-Lipschitz函数扩展到上半平面上的拟共形函数的唯一方式，且发现其他扩展形式属于该群作用的轨道。

初值问题解的存在性与唯一性的一个初等证明

An elementary proof of the existence and uniqueness of solutions to an initial value problem

本文用纯初等分析工具（不涉及积分）证明了Lipschitz条件下初值问题解的局部存在性与唯一性，通过Cauchy迭代在稠密子集收敛并延拓至全区间。

Zak Transform and non-uniqueness in an extension of Pauli's phase retrieval problem

The aim of this paper is to pursue the investigation of the phase retrieval problem for the fractional Fourier transform $\ff\_α$ started by the second author. We here extend a method of A.E.J.M Janssen to show that there is a countable set $\qq$ such that for every finite subset $å\subset \qq$, there exist two functions $f,g$ not multiple of one an other such that $|\ff\_αf|=|\ff\_αg|$ for every $α\in å$. Equivalently, in quantum mechanics, this result reformulates as follows: if $Q\_α=Q\cosα+P\sinα$ ($Q,P$ be the position and momentum observables), then $\{Q\_α,α\inå\}$ is not informationall…