We study convergence almost everywhere of multiple trigonometric Fourier series over cubes defined on the 𝑑-dimensional torus 𝕋𝑑. We provide a new approach which allows us to prove the novel ...

Let f ε L1(T). Define fα by fα(x) = f(x + α). Then the Fourier series of f is absolutely convergent if and only if there exists a Lebesgue point α for f such that both sequences $\langle(R_e ...

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...