相关论文: The covariogram and Fourier-Laplace transform in $…

We show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables…

Let $K$ and $K_0$ be convex bodies in $\mathbb{R}^d$, such that $K$ contains the origin, and define the process $(K_n, p_n)$, $n \geq 0$, as follows: let $p_{n+1}$ be a uniform random point in $K_n$, and set $K_{n+1} = K_n \cap (p_{n+1} +…

This work studies the Fourier transform of the characteristic function of planar convex bodies averaged over affine transformations. We establish lower and upper bounds on the latter quantities in terms of the geometric properties of the…

Let $K$ be a centrally-symmetric convex body in $\mathbb{R}^n$ and let $\|\cdot\|$ be its induced norm on ${\mathbb R}^n$. We show that if $K \supseteq r B_2^n$ then: \[ \sqrt{n} M(K) \leqslant C \sum_{k=1}^{n} \frac{1}{\sqrt{k}}…

Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…

An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,…

A procedure to determine the initial ansatz for the co-frame and spin connection characterizing a Riemann-Cartan geometry respecting a given group of continuous symmetries is illustrated. Given a particular group of symmetries and assuming…

All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…

The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in…

A new approach for solving the optical inverse problem of quantitative photoacoustic tomography is introduced, which interpolates between the well-known diffusion approximation and a radiative transfer equation based model. The proposed…

Interchanging character and co-character groups of a torus $T$ over a field $k$ introduces a contravariant functor $T \rightarrow \widehat{T}$. Interpreting $\rho:T\rightarrow {\mathbb C}^\times$, half the sum of positive roots for $T$ a…

The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…

The spherical Fourier transform on a harmonic Hadamard manifold $(X^n, g)$ of positive volume entropy is studied. If $(X^n, g)$ is of hypergeometric type, namely spherical functions of $X$ are represented by the Gauss hypergeometric…

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…

The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…

Let $K$ be a convex body in $\R^d$, let $j\in\{1, ..., d-1\}$, and let $\varrho$ be a positive and continuous probability density function with respect to the $(d-1)$-dimensional Hausdorff measure on the boundary $\partial K$ of $K$. Denote…

We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group $G$ over $\R$ acting on an affine $\R$-variety $V$, we consider the induced dual action on the coordinate ring $\R[V]$ and on…

We study the slicing inequality for the surface area instead of volume. This is the question whether there exists a constant $\alpha_n$ depending (or not) on the dimension $n$ so that $$S(K)\leq\alpha_n|K|^{\frac{1}{n}}\max_{\xi\in…

In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then…

If $\mathbb{F}_{q}$ is a finite field, $C$ is a vector subspace of $\mathbb{F}_{q}^{n}$ (linear code), and $G$ is a subgroup of the group of linear automorphisms of $\mathbb{F}_{q}^{n}$, $C$ is said to be $G$-invariant if $g(C)=C$ for all…