Related papers: Stability of Phase Retrievable Frames
In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions $\{\psi_{\lambda}\}_{\lambda\in \Lambda}\subset L^2(\mathbb{R}^d)$ that constitutes a semi-discrete frame, we ask…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals…
We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to…
Understanding the Higgs potential at large field values corresponding to scales in the range above $10^{10}{\rm GeV}$ is important for questions of vacuum stability, particularly in the early universe where survival of the Higgs vacuum can…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
Upon improving and extending the concept of redundancy of frames, we introduce the notion of redundancy of fusion frames, which is concerned with the properties of lower and upper redundancies. These properties are achieved by considering…
The short-time stability of concentration profiles in coherent periodic multilayers consisting of two components with large miscibility gap is investigated by analysing stationary solutions of the Cahn-Hilliard diffusion equation. The…
A vision foundation model outputs an embedding vector for an image, which can be affected by common editing operations (e.g., JPEG compression, brightness, contrast adjustments). These common perturbations alter embedding vectors and may…
Phase retrievability of a quantum channel asks whether pure states can be reconstructed from suitable measurements. In this paper, we study this problem from three complementary viewpoints: quantum information theory, operator-valued…
We consider the diffraction of time-harmonic plane waves by a periodic structure, governed by the Helmholtz equation. Bound states in the continuum (BICs) are quasi-periodic fields that remain $L^{2}$-bounded over one period and occur at…
We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems {with} jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set…
We study the stability of partitions in convex domains involving simultaneous coexistence of three phases, viz. triple junctions. We present a careful derivation of the formula for the second variation of area, written in a suitable form…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
In this article, we establish that any symmetric $m$-tensor field can be recovered pointwise from partial data of the $k$-th weighted divergent ray transform for any $k \in \mathbb{Z}^{+} \cup\{0\}$. Using the unique continuation property…
In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the…
In the weakened 16th Hilbert's Problem one asks for a bound of the number of limit cycles which appear after a polynomial perturbation of a planar polynomial Hamiltonian vector field. It is known that this number is finite for an individual…
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 study small perturbations of a sectional hyperbolic set of a vector field on a compact manifold. Indeed, we obtain robustly finiteness of homoclinic classes on this scenary. Moreover, since attractor and repeller sets are particular…
In this paper we consider the Gabor wave front set of ultradistributions in the frame of ultradifferentiable functions. We prove that such a wave front set, defined through a Gabor frame on a regular lattice, is not affected by…