Related papers: Basis-neutral Hilbert-space analyzers
We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…
This article constructs the Hilbert space for the algebra $\alpha \beta - e^{i \theta} \beta \alpha = 1 $ that provides a continuous interpolation between the Clifford and Heisenberg algebras. This particular form is inspired by the…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
A relativistic delay model for space very long baseline interferometry (hereafter SVLBI) observation of sources at infinite distance is derived. In SVLBI, where one station is on a spacecraft, the orbiting station's maximum speed in an…
We demonstrate two-step phase-shifting interferometry (holography) of complex laser modes generated by a spatial light modulator (SLM), in which the amplitude and phase of the signal are determined directly from measurements of…
We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…
It has been recently demonstrated that integrated optics could enhance accuracy, stability, and ease of use of stellar interferometry techniques. The subject of this thesis is the study of an optical component based on singlemode waveguides…
It is a commonly stated that the acceleration sensitivity of an atom interferometer is proportional to the space-time area enclosed between the two interfering arms. Here we derive the interferometric phase shift for an extensive class of…
The number of publications of aperture-synthesis images based on optical long-baseline interferometry measurements has recently increased due to easier access to visible and infrared interferometers. The interferometry technique has now…
Resolving fine details of astronomical objects provides critical insights into their underlying physical processes. This drives in part the desire to construct ever-larger telescopes and interferometer arrays and to observe at shorter…
The measurement of the gravitational lens delay time between light paths has relied, to date, on the source having sufficient variability to allow photometric variations from each path to be compared. However, the delay times of many…
In order to efficiently image a non-absorbing sample (a phase object), dedicated phase contrast optics are required. Typically, these optics are designed with the assumption that the sample is weakly scattering, implying a linear relation…
Infrared space interferometers can surpass the spatial resolution limitations of single-dish space telescopes. However, stellar interferometers from space have not been realized because of technical difficulties. Two beams coming from…
We develop a geometric framework for generalized Milnor classifying spaces in the setting of diffeological spaces and infinite-dimensional geometry. Starting from Milnor's construction, we introduce spherical and projective models endowed…
We theoretically consider ultracold polar molecules in a wave guide. The particles are bosons, they experience a periodic potential due to an optical lattice oriented along the wave guide and are polarised by an electric field orthogonal to…
In this paper we compare the performance of multi and single-mode interferometry for the estimation of the phase of the complex visibility. We provide a theoretical description of the interferometric signal which enables to derive the phase…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
Radio interferometry is an observational technique used to study astrophysical phenomena. Data gathered by an interferometer requires substantial processing before astronomers can extract the scientific information from it. Data processing…
The coherent superposition of orthogonal modes can result in transverse offsets, variations of the Rayleigh length and a reduction of the beam quality factor of the coherent sum of modes in comparison to the incoherent sum. Relations for…
Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by…