All Questions

A sequence of real functions $\{\phi_1,\cdots,\phi_n\}$ is called a Chebyshev system on an interval $I\subseteq\mathbb{R}$, if any real linear combination $\sum_{l=1}^n a_l\phi_l$ has at most $n-1$ ...

By a generalized trigonometric polynomial, I shall mean a function $f:\mathbb R^+ \rightarrow \mathbb R$ given by an expression of the form $$f(x) := \sum_{j=1}^k a_j \cos(\alpha_j x) + b_j \sin(\...

Let $$ f(x) = \sum_{j=1}^n c_j e^{2\pi i\alpha_j x}, g(x) = \sum_{k=1}^m d_k e^{2\pi i\beta_k x}$$ be two (quasi-periodic) trigonometric polynomials, where the coefficients $c_j, d_k$ are complex and ...

For $p=0,1,2,\dots$ and $n=0,1,2,\dots,$, let $f_{n,p}(z)=\sum_{k=0}^n k^p z^k$ be a sequence of polynomials. Restricted to the unit circle, the functions $g_{n,p}(t):=f_{n,p}(e^{it})$ are ...