Abstract
As we know, one of the main goals of this book has been to find a parametrization of the unit sphere of spaces of polynomials endowed with different norms whose unit balls can be described in \(\mathbb {R}^3\), but mainly we have tried to obtain the extreme polynomials of the unit balls. We have also studied some of the extreme polynomials in arbitrary dimensions and we have even described some of the extreme polynomials of arbitrary degree. The reason behind this is that a full description of the extreme polynomials of the unit ball has, as a matter of fact, can be applied to obtain many sharp polynomial inequalities (as we will see in this final chapter).
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Ferrer, J., García, D., Maestre, M., Muñoz, G.A., Rodríguez, D.L., Seoane, J.B. (2022). Applications. In: Geometry of the Unit Sphere in Polynomial Spaces. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-23676-1_9
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