Related papers: Vector Fourier analysis on compact groups and Assi…
It is well known that the category of Frolicher spaces and smooth mappings is Cartesian closed. The principal objective in this paper is to show that the full subcategory of Frolicher spaces that believe in fantasy that every Weil functor…
The composition of the Fourier transform in $\mathbb{R}^n$ with a suitable pseudodifferential operator is called a Fourier operator. It is compact in appropriate function spaces. The paper deals with its spectral theory. This is based on…
Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential…
In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier…
This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…
We define the Fourier transform of compactly supported Whittaker functions on a reductive p-adic group and we characterize the image of this transformation.
We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…
The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $\mathbb{R}^n$. The degree of compactness will be measured in terms of related entropy numbers. We are more…
We define a scalar valued Fourier transform for functions on the Heisenberg group and establish some of its basic properties like inversion formula, Plancherel theorem and Riemann-Lebesgue lemma. We also restate certain well known theorems…
The Fourier coefficients F(t) of a function f on a compact symmetric space U/K are given by integration of f against matrix coefficients of irreducible representations of U. The coefficients depend on a spectral parameter t, which…
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…
We prove that functions with compact support in non-quasianalytic classes of Roumieu-type and of Beurling-type defined by a weight matrix with some mild regularity conditions can be characterized by the decay properties of their Fourier…
The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important…
The Polymer Quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincar\'e invariant quantization by a singular one. This singular positive…
We introduce a scale of anisotropic Sobolev spaces defined through a three-parameter family of Fourier multipliers and study their functional analytic properties. These spaces arise naturally in PDE when studying traveling wave solutions,…
It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.
Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier…
The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…