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Maximizing a parametric integral over the unit sphere
I am trying to compute the nonnegative quantity
$$
\underset{y\in\mathbb{S}^{d-1}}{\sup}\int_{0}^{t}(\Vert A(\tau)y\Vert_{1}- \Vert A(\tau)y\Vert_{q})d\tau, \quad 1 < q < \infty
$$
where $\...
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