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arXiv · 2605.10535

On the existence of optimizers for nonlinear time-frequency concentration problems: the Born--Jordan distribution

Federico Stra·Erling A. T. Svela·S. Ivan Trapasso
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Abstract

We study the $L^p$ concentration problem for the Born--Jordan distribution in dimension $d>1$, thus extending the one-dimensional analysis in [Stra-Svela-Trapasso, J. Math. Pures Appl. (2026)]. We show that the existence of concentration optimizers depends on the exponent $p$ with a critical threshold at $p_*(d)= \frac{2d}{d-2}$ for $d\geq2$ (with the understanding that $p_*(2)=\infty$). In particular, for subcritical exponents $1\leq p p_*(d)$ we show that the functional is unbounded. We also provide the complete solution in the (significantly more) challenging critical regime in dimension $d=2$.

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Federico Stra, Erling A. T. Svela, S. Ivan Trapasso. 2026-05-11. On the existence of optimizers for nonlinear time-frequency concentration problems: the Born--Jordan distribution. https://arxiv.org/abs/2605.10535

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