因式分解两变量中的非负算子值三角多项式

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-06-27 DOI:10.1007/s00208-024-02895-9

Michael A. Dritschel

引用次数: 0

摘要

利用舒尔补码技术证明，在维数希尔伯特空间上，度数为 \((d_1,d_2)\)的两变量非负算子值三角多项式可以写成最多 \(2d_2\)解析多项式的赫米平方和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Factoring non-negative operator valued trigonometric polynomials in two variables

It is shown using Schur complement techniques that on dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree \((d_1,d_2)\) can be written as a sum of hermitian squares of at most \(2d_2\) analytic polynomials.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.