Related papers: Some topics in complex and harmonic analysis
Fourier series with absolutely summable coefficients provide a classical example of a commutative Banach algebra, and these notes are concerned with this and related matters.
In view of recent developments of the study of reproducing kernel Hilbert spaces, in particular with the context the Hardy spaces on tubes, aspects of rational approximation for functions of finite energy in several complex and several real…
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing…
We investigate some properties of balayage of charges and measures for subclasses of subharmonic functions and their relationship to the geometry of domain or open set in finite-dimensional Euclidean space where this balayage is considered.
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
Several interesting formulas concerning finite Hilbert transform and logarithmic integrals are proved with application in determining equilibrium measures, planar limits of analytic random matrix models with $1-$cut potential and solving…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
We analyze on the formalism of probability measures -functional integrals on function spaces , the problem of infinities on Euclidean field theories
A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to…
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.
We continue our discussion from part I.
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
In the digital world, signals are discrete and finite. The Fourier representation of discrete and finite signals is FT convolution of the finite sampling function and the continuous signal. Conventionally, finite sampling is treated as a…
The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.
We generalize to the case of compactified superstrings a construction given previously for critical superstrings of finite one loop amplitudes that are well-defined for all external momenta. The novel issues that arise for compactified…
We introduce quasi-Prufer extensions of rings in order to relativize the notion of quasi-Prufer domains and to take into account some contexts recently introduced in the literature. We also introduce almost-Prufer ring extensions.…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…