相关论文: Holomorphic transforms with application to affine …

We study the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or…

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…

This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…

In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…

We introduce a new modality for dynamic phase imaging in confocal microscopy based on synthetic optical holography. By temporal demultiplexing of the detector signal into a series of holograms, we record time-resolved phase images directly…

Local Fourier analysis is a commonly used tool to assess the quality and aid in the construction of geometric multigrid methods for translationally invariant operators. In this paper we automate the process of local Fourier analysis and…

Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…

For each $f\!:\!\mathbb{R}\to\mathbb{C}$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrable functions in the Alexiewicz norm, it is shown that the…

In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or…

Variational Autoencoders (VAEs) are powerful generative models, however their generated samples are known to suffer from a characteristic blurriness, as compared to the outputs of alternative generating techniques. Extensive research…

Let $E(\mathscr{A})$ denote the shift-invariant space associated with a countable family $\mathscr{A}$ of functions in $L^{2}(\mathbb{H}^{n})$ with mutually orthogonal generators, where $\mathbb{H}^{n}$ denotes the Heisenberg group. The…

In order to define a geometric Fourier transform, one usually works with either $\ell$-adic sheaves in characteristic $p>0$ or with $D$-modules in characteristic 0. If one considers $\ell$-adic sheaves on the stack quotient of a vector…

We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…

This article introduces Levy-driven graph supOU processes, a parsimonious parametrisation for high-dimensional time series in which dependence between components is governed by a graph structure. Specifically, the model bridges short- and…

In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…

We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by deriving inversion formulas for the divergent beam transform and…

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a…

We introduce an elementary method for proving the absolute continuity of the time marginals of one-dimensional processes. It is based on a comparison between the Fourier transform of such time marginals with those of the one-step Euler…