This is called a uniqueness theorem because it has as an immediate corollary the fact that a 2iT periodic complex valued function of a real variable coincides with the values of at most one …

The uniqueness and the zeros of trigonometric series was an active area of research in 19th century Europe.

May 28, 2023 · But what can be said about the uniqueness of a trigonometric series? If we can represent a function \(f\) as a general trigonometric series \[f(x) = \sum_{n=0}^{\infty } (a_n\cos …

Jun 7, 2020 · A set $ E \subset [ 0, 2 \pi ] $ is called a set of uniqueness (cf. Uniqueness set), or a $ U $- set, if the convergence everywhere on $ [ 0, 2 \pi ] $ of a trigonometric series to zero …

Jan 25, 2019 · Consider the equation \begin{cases} \displaystyle y'(x)=\cos\left(y(x)\right)\\ y(0)=0 \end{cases} I've found explicitely $y$ and I know this equation has a unique solution. However …

the uniqueness of solutions to the heat equation and its justification. where the diffusion constant k > 0, and the functions a(t), b(t), and f(x) are C2 (twice continuously differentiable) on their …

May 17, 2024 · Is there any elementary way to prove that these basic differential equations have a unique solution? By elementary, I mean using the definitions and basic properties of …

In this paper we clarify a problem concerning uniqueness of the polynomial which best approximates cos kx in the L metric with respect to a trigonometric system of order n in which …

In many particular cases, by using special devices one can nd formulas for the solutions { but it is far from obvious that a solution exists or is unique. In fact, there are simple examples showing …

There exists a unique polynomial $P_{n}$ such that for all $t \in [0,\frac{\pi}{2}]$, $P_{n}(\operatorname{cotan}^2t)=\frac{\sin((2n+1)t}{(\sin t)^{2n+1}}$ with …