Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the truncated multidimensional moment problems in $\mathbb{C}^n$ (2102.04495v2)

Published 8 Feb 2021 in math.FA

Abstract: We consider the problem of finding a (non-negative) measure $\mu$ on $\mathfrak{B}(\mathbb{C}n)$ such that $\int_{\mathbb{C}n} \mathbf{z}{\mathbf{k}} d\mu(\mathbf{z}) = s_{\mathbf{k}}$, $\forall \mathbf{k}\in\mathcal{K}$. Here $\mathcal{K}$ is an arbitrary finite subset of $\mathbb{Z}n_+$, which contains $(0,...,0)$, and $s_{\mathbf{k}}$ are prescribed complex numbers (we use the usual notations for multi-indices). There are two possible interpretations of this problem. At first, one may consider this problem as an extension of the truncated multidimensional moment problem on $\mathbb{R}n$, where the support of the measure $\mu$ is allowed to lie in $\mathbb{C}n$. Secondly, the moment problem is a particular case of the truncated moment problem in $\mathbb{C}n$, with special truncations. We give simple conditions for the solvability of the above moment problem. As a corollary, we have an integral representation with a non-negative measure for linear functionals on some linear subspaces of polynomials.

Summary

We haven't generated a summary for this paper yet.