Related papers: Mapping properties of Fourier transforms, II
One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then the harmonic…
A mathematical relation between elements of one- and multi-dimensional discrete Fourier transforms (DFT) is found. A method of analysing the multi-dimensional data by their single one-dimensional (1-D) DFT is offered. An experiment of…
We give an explicit description of the set of all factorization structures, or twisting maps, existing between the algebras k^2 and k^2, and classify the resulting algebras up to isomorphism. In the process we relate several different…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
Some fixed point results are given for a class of functional contractions over partial metric spaces. These extend some contributions in the area due to Ilic et al [Math. Comput. Modelling, 55 (2012), 801-809].
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of…
Recently, we have studied the Finsler space with h-Matsumoto change and found Cartan connection for the transformed space [2]. In this paper, we have discussed certain geometrical properties of the hypersurface of a Finsler space for the…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
In this paper, we will study the continuity of the Fourier transform of measures with respect to the vague topology. We show that the Fourier transform is vaguely discontinuous on R, but becomes continuous when restricting to a class of…
Certain relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The widest subspaces of the space of functions of bounded variation are indicated in which the…
In this manuscript, we claim that the newly introduced $\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\mathcal{F}$-metric space is second countable. Additionally, we acquire…
In this paper, we introduce soft continuous mappings which are defined over an initial universe set with a fixed set of parameters. Later we study soft open and soft closed mappings, soft homeomorphism and investigate some properties of…
In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.
It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after…
We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show…
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 a help of a family of weight functions is considered in the paper. For this…
These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…
We characterise modulation spaces by suitable Wiener estimates on the short-time Fourier transforms of the involved functions and distributions. We use the results to refine some formulae on periodic distributions with Lebesgue estimates on…