Related papers: Reflections on the q-Fourier transform and the q-G…
We survey and investigate some computational aspects of the Fourier-Mukai transform.
In a paper by Umarov, Tsallis and Steinberg (2008), a generalization of the Fourier transform, called the $q$-Fourier transform, was introduced and applied for the proof of a $q$-generalized central limit theorem ($q$-CLT). Subsequently,…
This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…
We describe positive generalized functionals in Gaussian Analysis. We focus on distribution spaces larger than the space of Hida Distributions. It is shown that a positive distribution is represented by a measure with specific growth of its…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Quasicrystals are tempered distributions $\mu$ which satisfy symmetric conditions on $\mu$ and $\widehat \mu$. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…
We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
A q-version of the Fourier transformation and some of its properties are discussed.
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
In this work, we generalize the results of Naber about the Fractionary Schr\"{o}dinger Equation with the use of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…
Computations in high-dimensional spaces can often be realized only approximately, using a certain number of projections onto lower dimensional subspaces or sampling from distributions. In this paper, we are interested in pairs of…
In this paper we study an analytic Yeh--Feynman integral and an analytic Yeh--Fourier--Feynman transform associated with Gaussian processes. Fubini theorems involving the generalized analytic Yeh--Feynman integrals are established. The…
In a first part, we give a method for solving a family of fuchsian systems of operators of pseudo-derivations associated to a family of homographies with two parameters which unify and generalize the differential, the difference and the…