Related papers: Phase-isometries between normed spaces

Phase retrieval has become a very active area of research. We will classify when phase retrieval by Parseval frames passes to the Naimark complement and when phase retrieval by projections passes to the orthogonal complements. We introduce…

A study is made of linear isometries on Fr\'echet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the…

Conformally compactified phase space is conceived as an automorphism space for the global action of the extended conformal group. Space time and momentum space appear then as conformally dual, that is conjugate with respect to conformal…

Given a metrizable space $Z$, denote by ${\rm PM}(Z)$ the space of continuous bounded pseudometrics on $Z$, and denote by ${\rm AM}(Z)$ the one of continuous bounded admissible metrics on $Z$, the both of which are equipped with the…

A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected…

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase…

Let $\mathcal{I}$ be an ideal on $\mathbb{N}$. A mapping $f:X\to Y$ is called an $\mathcal{I}$-covering mapping provided a sequence $\{y_{n}\}_{n\in\mathbb N}$ is $\mathcal{I}$-converging to a point $y$ in $Y$, there is a sequence…

The two output signals of quadrature phase interferometers allow to benefit both from the high sensitivity of interferometry (working inside a fringe) and from an extended input range (counting fringes). Their calibration to reach a linear…

In this paper, we consider the quantum-mechanical phase space patterns on ordered and disordered networks. For ordered networks in which each node is connected to its 2m nearest neighbors (m on either side), the phase space…

We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…

Let X be a compact (resp. compact and nonsingular) real algebraic variety and let Y be a homogeneous space for some linear real algebraic group. We prove that a continuous (resp. C^infinity) map f:X-->Y can be approximated by regular maps…

A space $X$ is called $CCS$-normal space if there exist a normal space $Y$ and a bijection $f: X\mapsto Y$ such that $f\lvert_C:C\mapsto f(C)$ is homeomorphism for any cellular-compact subset $C$ of $X$. We discuss about the relations…

Consider a finite morphism f:X -> Y of smooth projective varieties over a finite field k. Suppose X is the vanishing locus in projective N-space of at most r forms of degree at most d. We show there is a constant C, depending only on N, r,…

On the basis of the data given in the works of different authors a criterion of phase-photometric method of measurement of energy angle of divergence has been formulated. Validity of application of the obtained relations for a ray beam with…

In this paper we deal with the convergence of sequences of positive linear maps to a (not assumed to be linear) isometry on spaces of continuous functions. We obtain generalizations of known Korovkin-type results and provide several…

A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold $X$ is a normal stratified pseudomanifold $Y$ together with a finite-to-one projection $n:Y\to X$ satisfying a local condition…

We consider the Ising model on $\mathbb Z\times \mathbb Z$ where on each horizontal line $\{(x,i), x\in \mathbb Z\}$, the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\gamma(x,y)\sim \gamma J(\gamma…

A metric space $\mathrm{M}=(M,\de)$ is {\em indivisible} if for every colouring $\chi: M\to 2$ there exists $i\in 2$ and a copy $\mathrm{N}=(N, \de)$ of $\mathrm{M}$ in $\mathrm{M}$ so that $\chi(x)=i$ for all $x\in N$. The metric space…

Let $X$, $Y$ be two real Banach spaces, and $\eps\geq0$. A map $f:X\rightarrow Y$ is said to be a standard $\eps$-isometry if $|\|f(x)-f(y)\|-\|x-y\||\leq\eps$ for all $x,y\in X$ and with $f(0)=0$. We say that a pair of Banach spaces…

We classify affine operators on a unitary or Euclidean space U up to topological conjugacy. An affine operator is a map f: U-->U of the form f(x)=Ax+b, in which A: U-->U is a linear operator and b in U. Two affine operators f and g are said…