5 problems

Let $d\in\mathbb{N}$, let $\widehat{f}$ denote the unitary Fourier transform of $f\in\mathcal{L}^2(\mathbb{R}^d)$, and for $f\in\mathcal{L}^2(\mathbb{R}^d)\setminus\{0\}$ define it…

Let $w$ be a positive unit-integrable weight on $[-1,1]$, and let p_n_{n\geq 0} be the corresponding sequence of orthonormal polynomials. Define … The Beckermann et al. conjectur…

Let $A$ be a Sidon set in an ambient abelian group, and let $X$ and $Y$ be independent random variables taking values in $A$. Let $H$ denote Shannon entropy. Ajjanagadde's conjectu…

Inflection-point conjecture. There exists an inflection point $\chi_n(\alpha)\in\bigl(H_{\text{\scriptsize \boldmath }v_n}(\mathrm{e}^{-n}),\ln n\bigr)$ such that…

Alternating-sign conjecture. The signs of all subsequent derivatives of $H(X+Z_t)$ alternate, extending the explicitly verified alternating-sign property through order four.