Related papers: Phase space localizing operators
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
The first three results in this thesis are motivated by a far-reaching conjecture on boundedness of singular Brascamp-Lieb forms. Firstly, we improve over the trivial estimate for their truncations, thus excluding potential trivial…
We study mixed-state localization operators from the perspective of Werner's operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase…
In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and…
Given a space of homogeneous type we give sufficient conditions on a variable exponent {p(.)} so that the fractional maximal operator {M_{\eta}} maps {L^{p(.)}(X)} to {L^{q(.)}(X)}, where {1/p(.) - 1/q(.) = {\eta}}. In the endpoint case we…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
We introduce new classes of modulation spaces over phase space. By means of the Kohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operators that bound their operator norms on $L^p$-spaces, Sobolev spaces, and…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
Motivated by both concepts of R.J. Adler's recent work on utilizing Clifford algebra as the linear line element $ds = \left\langle \gamma_\mu \right\rangle dX^\mu $, and the fermionization of the cylindrical worldsheet Polyakov action, we…
The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the $x$-margin are polynomials of the position…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…
New effective operators, describing the photons with given polarization at given position with respect to a source are proposed. These operators can be used to construct the near and intermediate zones quantum optics. It is shown that the…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
The phase space $S\times Z$ for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
A complex function is associated to each bounded linear operator
The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta who developed a formalism to calculate the electronic polarization as an…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…