Related papers: Examples of H\"older-stable Phase Retrieval

Let $N\in\mathbb{N}$ and $u$ be a weak solution of equation $\displaystyle Lu\equiv - \sum_{i,j=1}^{N}\frac{\partial}{\partial x_{j}}(\frac{\partial u}{\partial x_{i}}b^{ij})= f$ in $\Omega\subset \mathbb{R}^{N}$. We obtain functions $G$…

Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in $\SL(2,\ZZ)$. It is…

Given an one-dimensional Lorenz-like expanding map we prove that the condition\linebreak $P_{top}(\phi,\partial \mathcal{P},\ell)<P_{top}(\phi,\ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied…

We study the determination of functions in Fock space from samples of their absolute value, known as the phase retrieval problem in Fock space. An important finding in this research field asserts that phaseless sampling on lattices of…

Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…

In spacetime dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu-Goldstone modes described by fields with values in G/H. In two-dimensional spacetimes…

We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…

In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set $\fc$ of $m$ vectors in the complex Hilbert space of dimension n allows for…

In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods are constructed by letting a piecewise $k$-th order ($k\ge…

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…

We show that for any probability measure \mu there exists an equivalent norm on the space L^1(\mu) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This…

The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of K\"ahler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting'…

We show that bounded solutions of the quasilinear elliptic equation $\Delta_{p(x)} u=g+div(\textbf{F})$ are locally H\"{o}lder continuous provided that the functions $g$ and $\textbf{F}$ are in suitable Lebesgue spaces.

We investigate the H\"older continuity of solutions to stochastic partial differential equations of the form $\frac{\partial u}{\partial t}=\mathcal{L}u+\sigma(u)\dot{F}$, subject to a suitable initial condition. The noise term $\dot{F}$ is…

For various function spaces of the form gU or U+gV, U and V e.g. almost periodic functions AP, (bounded) uniformly continuous functions BUC, UC, g(t) = exp(it^2), their properties are discussed, especially a Loomis type condition (Delta)…

We prove H\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV}…

We consider the impact of colored scalars that can couple directly to matter fields on the recently measured h to gamma gamma excess. Among all possible candidates only scalar states transforming as (8, 2,1/2) and (6,3,1/3) under the…

A closed real subspace V of a complex Hilbert space H is called standard if V intersects iV trivially and and V + i V is dense in H. In this note we study several aspects of the geometry of the space Stand(H) of standard subspaces. In…

We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…

We prove local H\"older regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+sp}}\,dy=0, \end{align*} for $p\in…