Related papers: Characterisation of the Weyl-H\"ormander classes b…

We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz…

It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short paper we give complete characterisations of initial wave front…

Let $g$ be a complex semisimple Lie algebra with Weyl group $W$. Let $H(W)$ be the Iwahori-Hecke algebra associated to $W$. For each $w\in W$, let $T_w$ and $C_w$ be the corresponding $Z$-graded twisting functor and $Z$-graded shuffling…

Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier…

Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…

New methods are proposed to characterize the spectral-temporal distribution of single photons. The presented protocols take advantage of spectral filtering, frequency entanglement between two single photons the one of interest and a…

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…

A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down…

We study the harmonic representation of $SU(p,q)$ in connection to the complex Weyl correspondence on the Fock space. In particular, we give explicit formulas for the complex Weyl symbols of the harmonic representation operators. Similar…

We prove several characterizations of the Hardy spaces for Fourier integral operators $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, for $1<p<\infty$. First we characterize $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ in terms of…

We perform a Wigner analysis of Fourier integral operators (FIOs), whose main examples are Schr\"odinger propagators arising from quadratic Hamiltonians with bounded perturbations. The perturbation is given by a pseudodifferential operator…

We discuss the structural and topological properties of a general class of weighted $L^1$ convolutor spaces. Our theory simultaneously applies to weighted $\mathcal{D}'_{L^1}$ spaces as well as to convolutor spaces of the Gelfand-Shilov…

We study the topological dynamics of the action of the diagonal subgroup on quotients Gamma\PSL(2,R)*PSL(2,R), where Gamma is an irreducible lattice. Closed orbits are described and a set of points of dense orbit is explicitly given. Such…

We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…

We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as…

We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\eta)$ are elements of $C^{r}_{*}S^{m}_{1,\delta}$ classes that have limited regularity in the…

We show rigidity results for the operator equations T(f.g) = Tf.Tg, T(f*g) = Tf.Tg and T(f.g) = Tf*Tg for bijective operators T acting on sufficently large spaces of smooth functions. Typically a condition like |T(f.g) - Tf.Tg| < a for all…

In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter H\"ormander class $S^{\vec m}( \mathbb{R}^\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase…

We give a brief survey of recent results concerning almost diagonalization of pseudodifferential operators via Gabor frames. Moreover, we show new connections between symbols with Gevrey, analytic or ultra-analityc regularity and…

We introduce an $O(M)$ algorithm for evaluating the azimuthal Fourier modes $G_{k,m}$, $m = 0, 1, ..., M$, of the three-dimensional Helmholtz Green's function with real wavenumber $k$, together with all their first- and second-order…