S. Ivan Trapasso

@workingpaper{SST_26,

title = {On the existence of optimizers for nonlinear time-frequency concentration problems: the Born-Jordan distribution},

author = {Federico Stra and Erling Svela and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2605.10535, arXiv},

year  = {2026},

date = {2026-05-12},

urldate = {2026-05-12},

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 (dgeq2) (with the understanding that (p_*(2)=infty)). In particular, for subcritical exponents (1leq p<p_*(d)) we prove that the supremum is finite and is attained, whereas for supercritical exponents (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).},

keywords = {Born-Jordan quantization, concentration problems, quantum harmonic analysis, time-frequency analysis, time-frequency distributions},

pubstate = {published},

tppubtype = {workingpaper}

}