Flat extensions of positive moment matrices : recursively generated relations
Author(s)
Bibliographic Information
Flat extensions of positive moment matrices : recursively generated relations
(Memoirs of the American Mathematical Society, no. 648)
American Mathematical Society, 1998
Available at 19 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"November 1998, volume 136, number 648 (third of 6 numbers)." -- t.p.
Includes bibliographical references
Description and Table of Contents
Description
In this book, the authors develop new computational tests for existence and uniqueness of representing measures $\mu$ in the Truncated Complex Moment Problem: $\gamma_{ij}=\int \bar z^iz^j\, d\mu$ $(0\1e i+j\1e 2n)$. Conditions for the existence of finitely atomic representing measures are expressed in terms of positivity and extension properties of the moment matrix $M(n)(\gamma)$ associated with $\gamma \equiv \gamma ^{(2n)}$: $\gamma_(00), \dots, \gamma_{0,2n},\dots, \gamma _{2n,0}$, $\gamma_{00}>0$.This study includes new conditions for flat (i.e., rank-preserving) extensions $M(n+1)$ of $M(n)\ge 0$; each such extension corresponds to a distinct rank $M(n)$-atomic representing measure, and each such measure is minimal among representing measures in terms of the cardinality of its support. For a natural class of moment matrices satisfying the tests of recursive generation, recursive consistency, and normal consistency, the existence problem for minimal representing measures is reduced to the solubility of small systems of multivariable algebraic equations.In a variety of applications, including cases of the quartic moment problem ($n=2$), the text includes explicit contructions of minimal representing measures via the theory of flat extensions. Additional computational texts are used to prove non-existence of representing measures or the non-existence of minimal representing measures. These tests are used to illustrate, in very concrete terms, new phenomena, associated with higher-dimensional moment problems that do not appear in the classical one-dimensional moment problem.
Table of Contents
Introduction Flat extensions for moment matrices The singular quartic moment problem The algebraic variety of $\gamma$ J. E. McCarthy's phenomenon and the proof of Theorem 1.5 Summary of results Bibliography List of symbols.
by "Nielsen BookData"