Related papers: Adventures in harmonic analysis
A walker is the association of a sub-millimetric bouncing drop moving along with a co-evolving Faraday wave. When confined in a harmonic potential, its stable trajectories are periodic and quantised both in extension and mean angular…
Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…
A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the…
We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.
In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.
In this paper we analyze some classical operators in harmonic analysis associated to the multidimensional discrete Laplacian \[ \Delta_N f(\mathbf{n})=\sum_{i=1}^{N}(f(\mathbf{n}+\mathbf{e}_i)-2f(\mathbf{n})+f(\mathbf{n}-\mathbf{e}_i)),…
This note shows how to align a periodic signal with its the Fourier transform by means of frequency or time scaling. This may be useful in developing new algorithms, e.g. for pitch estimation. This note also convolves the signals and the…
These notes, associated with a topics course, are concerned with some general methods related to norms and linear transformations.
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
This paper is concerned with the study of mean field games master equations involving an additional variable modelling common noise. We address cases in which the dynamics of this variable can depend on the state of the game, which requires…
This text proposes geometrical descriptions of all variational problems invariant by conformal transformations in two variables. First a characterisation in terms of C-Finsler manifolds, a suitable generalization of Finsler manifolds, is…
We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integral quantizations, and affine quadratic time-frequency…