Related papers: Adventures in harmonic analysis
The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
These informal notes, initially prepared a few years ago, look at various questions related to infinite processes in several parts of mathematics, with emphasis on examples.
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…
This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
This article describes a laboratory or demonstration technique employing the bass guitar and a Vernier LabPro (or a PC soundcard) for teaching wave physics and introducing Fourier analysis. The Fourier transform of an open string provides a…
Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2,…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
These informal notes deal with p-adic versions of Heisenberg groups and related matters.
These notes, associated with a topics course, deal with some special cases involving norms and linear transformations.
This manuscript surveys quantum operations under the influence of harmonic magnetic fields subject to time variations. The author scrutinises the dynamic interplay of these fields and canonical variables, leading to effects such as…
The notes contain a streamlined account on stability of univariate polynomials and related problems
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…
A q-version of the Fourier transformation and some of its properties are discussed.
A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system {x,v} with additive white noise is analyzed numerically. A…