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Let $p=a_{0}+a_{1}z+\ldots+a_{n}z^{n}$ be a polynomial. Consider the following truncated $\ell^{1}$-seminorm of the coefficients of $p$: $$\|p\|_{\ell^{1},\text{trun.}}:=\sum_{k=1}^{n}|a_{k}|=\|p-a_{0}...

Let $a,b$ two real numbers, $\theta$ a real parameter and suppose that you have an analytic function of the form: $$ f_\theta(x)\triangleq \sum_{k\in\mathbb{N}}a_k(\theta)x^k \quad\forall x\in[a,b], $$...