Related papers: Images of function and distribution spaces under t…
We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on…
Using the existence of infinite numbers $k$ in the non-Archimedean ring of Robinson-Colombeau, we define the hyperfinite Fourier transform (HFT) by considering integration extended to $[-k,k]^{n}$ instead of $(-\infty,\infty)^{n}$. In order…
In this paper the p -adic Lizorkin spaces of test functions and distributions are introduced, and multidimensional Vladimirov's and Taibleson's fractional operators are studied on these spaces. Since the p -adic Lizorkin spaces are…
Classical tests are available for the two-sample test of correspondence of distribution functions. From these, the Kolmogorov-Smirnov test provides also the graphical interpretation of the test results, in different forms. Here, we propose…
In this papae we introduce and investigate new 2-microlocal spaces associated with Besov type and Triebel-LIzorkin type spaces. We establish characterizations of these function spaces via the phi transform, the atom and molecular…
Within Bishop Set Theory, a reconstruction of Bishop's theory of sets, we study the so-called completely separated sets, that is sets equipped with a positive notion of an inequality, induced by a given set of real-valued functions. We…
A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…
We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…
This paper is a survey of a new family of Banach spaces ${KS}^2$ and $SD^2$ that provide the same structure for the Henstock-Kurzweil (HK) integrable functions as the $L^p$ spaces provide for the Lebesgue integrable functions. These spaces…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional…
We consider a family of Besov spaces of analytic type on the Shilov boundary $\mathcal{N}$ of a homogeneous Siegel domain $D$, and study their properties in relation to convolution, Fourier multipliers, and complex interpolation. In…
In this paper, we investigate fractional B splines and their connections with Fourier analysis, and establish connections with generalized Stirling-type numbers and distribution theory. Employing a generating function approach inspired by…
We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a Burkholder type inequality in a dual norm. The theory we…
The aim of the present paper is three folds. For a reproducing kernel Hilbert space $\mathcal{A}$ (R.K.H.S) and a $\sigma-$finite measure space $(M_{1},d\mu_{1})$ for which the corresponding $L^{2}-$space is a separable Hilbert space, we…
The primary motivation behind this paper is an attempt to provide a thorough explanation of how the Mellin transform arises naturally in a process akin to the construction of the celebrated Gelfand transform. We commence with a study of a…
Triangle partition maps form a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This paper begins the exploration of the functional analysis behind the transfer operator of each of these…
Inspired from the Cholewinski approach see [5], we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well as some associated quaternionic linear operators. In a particular case, we reobtain the slice…
Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L^2-case, such an equivalence follows from the unitarity of the polyanalytic Bargmann transform. We will…
On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and…