Let C-d,C-n be the convex cone consisting of real n-variate degree d forms that are strictly positive on R-n {0}. We prove that the Lebesgue volume of the sublevel set {g <= 1} of g is an element of C-d,n is a completely monotone function on C-d,C-n and investigate the related properties. Furthermore, we provide (partial) characterization of forms whose sublevel sets have finite Lebesgue volume.
Volumes of Sublevel Sets of Nonnegative Forms and Complete Monotonicity / Kozhasov, Khazhgali; Lasserre, Jean B.. - In: SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY. - ISSN 2470-6566. - 7:4(2023), pp. 768-785. [10.1137/22m1502458]
Volumes of Sublevel Sets of Nonnegative Forms and Complete Monotonicity
Kozhasov, Khazhgali;
2023-01-01
Abstract
Let C-d,C-n be the convex cone consisting of real n-variate degree d forms that are strictly positive on R-n {0}. We prove that the Lebesgue volume of the sublevel set {g <= 1} of g is an element of C-d,n is a completely monotone function on C-d,C-n and investigate the related properties. Furthermore, we provide (partial) characterization of forms whose sublevel sets have finite Lebesgue volume.| File | Dimensione | Formato | |
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