Prof. Élodie Cartan \today Introduction Integral transforms, whose historical prototype is the Fourier transform, have been a central tool in mathematical analysis for two centuries. Their development, initiated by Fourier (1822) and fully axiomatized by Schwartz (1950) within the framework of distributions, now finds profound echoes in operator theory and noncommutative geometry. This article synthesizes… Continue reading Integral Transforms and Spectral Analysis: A Modern Perspective
Bernoulli Polynomials
1. Introduction Bernoulli polynomials, introduced by Swiss mathematician Jacob Bernoulli in the 17th century, form a fundamental family of polynomials in mathematics. They appear in various fields such as number theory, mathematical analysis, and symbolic computation. Defined through a generating function, these polynomials are closely related to Bernoulli numbers, which are coefficients appearing in Taylor… Continue reading Bernoulli Polynomials