Related papers: Spaces of Analytical Functions and Wavelets--Lectu…
In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the…
The area of Fourier analysis connected to signal processing theory has undergone a rapid development in the last two decades. The aspect of this development that has received the most publicity is the theory of wavelets and their relatives,…
Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his theory of monogenic functions, a generalisation of…
The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to…
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are…
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
We use reflections involving analytic Dirichlet and Neumann data on a real-analytic curve in order to find a representation of solutions to Cauchy problems for harmonic functions in the plane. We apply this representation for finding…
This paper is concerned with the study of a class of nonlinear nonlocal functional evolution problems defined in an abstract Banach algebra. We introduce an abstract functional setting that encompasses a wide range of structured population…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative…
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions within these spaces, and in particular, we provide an…
In this paper, we focus on how we can interpret the actions of the elements in the Gelfand spectrum of a weighted Fourier algebra on connected Lie groups. They can be viewed as evaluations on specific points of the complexification of the…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
Nowadays the theory and application of wavelet decompositions plays an important role not only for the study of function spaces (of Lebesgue, Hardy, Sobolev, Besov, Triebel-Lizorkin type) but also for its applications in signal and…
The main goal of this work is to present a detailed study of the foundations of Complex Geometry, highlighting its geometrical, topological and analytical aspects. Beginning with a preliminary material, such as the basic results on…
The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…
For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.