Geometry of the Unit Sphere in Polynomial Spaces

“This book is the pictorial description of the unit sphere in 3-dimensional cases, which motivates analytic build-up in higher dimensions. This facilitates the reader's perception of the extreme point analysis of the polynomial spaces from a visual perspective. The extreme points of the polynomial spaces are crucial in studying polynomial inequalities. The classification of extreme points in polynomial spaces has a rich background in the literature. This book culminates in state-of-the-art results in this field of research.” (Saikat Roy, Mathematical Reviews, June, 2025)