Abstract
Abstract
We show that the Euclidean ball has the smallest volume among sublevel sets of nonnegative forms of bounded Bombieri norm as well as among sublevel sets of sum of squares forms whose Gram matrix has bounded Frobenius or nuclear (or, more generally, p-Schatten) norm. These volume-minimizing properties of the Euclidean ball with respect to its representation (as a sublevel set of a form of fixed even degree) complement its numerous intrinsic geometric properties. We also provide a probabilistic interpretation of the results.
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Software
Reference18 articles.
1. Agmon, S.: The $${L}_p$$ approach to the Dirichlet problem. Part I: regularity theorems. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 13(4), 405–448 (1959)
2. Agrachev, A.A., Kozhasov, Kh., Uschmajew, A.: Chebyshev polynomials and best rank-one approximation ratio (2019).
arXiv:1904.00488
3. Brachat, J., Comon, P., Mourrain, B., Tsigaridas, E.: Symmetric tensor decomposition. Linear Algebra Appl. 433(11), 1851–1872 (2010)
4. Choi, M.D., Lam, T.Y., Reznick, B.: Sums of squares of real polynomials, $$K$$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992). In: Proceedings Symposia in Pure Mathematics of the American Mathematical Society, Providence, RI, vol. 58, pp. 103–126 (1995)
5. Eckart, C., Young, G.: The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献