All Questions

Assume that $J$ is the interval $(-\pi,\pi]$. For $k=1,\ldots,2n$, suppose that $\lambda_k$s are real functions on $J$ with $|\lambda_k|=1$, meaning that $\lambda_k(t)$ is either $-1$ or $1$ where $t\...

Problem: Let $f\colon \mathopen[0,1\mathclose] \to \mathbb{R}$ be defined as $$ f(x) = \frac{e^{\rho x}-1}{e^{\rho x}-1+e^{\rho (1-\gamma x)}-e^{\rho (1-\gamma) x}} $$ where $\rho$ and $\gamma$ are ...

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(\...

Suppose we are given an exponential polynomial $f:\mathbb{R}\mapsto\mathbb{R}$ $$ f(t)=\sum_{i=1}^n p_i(t)e^{\lambda_i t} $$ where $p_i(t)$s are polynomials with algebraic coefficients and $\lambda_i$...

I'm going to define an exponential polynomial of degree $k$ as a function $f$ of the form $f(x) = \sum_{i=1}^k c_ie^{\alpha_ix}$ ($\alpha_i$s real). My first question is: is there an algorithm for ...