The $\mathbf {K}$-moment problem for continuous linear functionals

The K-moment Problem for Continuous Linear Functionals

Given a closed (and non necessarily compact) basic semialgebraic set K ⊆ R, we solve the K-moment problem for continuous linear functionals. Namely, we introduce a weighted l1-norm lw on R[x], and show that the lw-closures of the preordering P and quadratic module Q (associated with the generators of K) is the cone Psd(K) of polynomials nonnegative on K. We also prove that P and Q solve the K-m...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The Cauchy problem for linear growth functionals

A moment problem for pseudo-positive definite functionals

A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudopositive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure. The second main result is a characterization of determinacy in the class of equivalent pseudo-positive representation measures. Finally ...

The truncated K-moment problem for closure of open sets

We consider the truncated K-moment problem when K ⊆ Rn is the closure of a, not necessarily bounded, open set (which includes the important cases K = Rn and K = Rn+). We completely characterize the interior of the convex cone of finite sequences that have a representing measure on K ⊆ Rn. It is in fact the domain of the Legendre-Fenchel transform associated with a certain convex function. And s...