Generalized Tchakaloff’s Theorem for Semi-spectral Measures

نویسندگان

  • LIH-CHUNG WANG
  • Joseph A. Ball
  • CHIH-RUNG CHEN
چکیده

We proved the existence of exact quadrature formulae with semipositive definite coefficient matrices for polynomials of prescribed degree in n variables and with respect to a semi-spectral measure. Our proof could be viewed as a direct translation (generalization) of Putinar’s result on the existence of quadrature formulae for a positive measure without compact support.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Proof of Tchakaloff’s Theorem

We provide a simple proof of Tchakaloff’s Theorem on the existence of cubature formulas of degree m for Borel measures with moments up to order m. The result improves known results for non-compact support, since we do not need conditions on (m + 1)st moments. We consider the question of existence of cubature formulas of degree m for Borel measures μ, where moments up to order m exist: Definitio...

متن کامل

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

متن کامل

Compressed sampling inequalities by Tchakaloff’s theorem

We show that a discrete version of Tchakaloff’s theorem on the existence of positive algebraic cubature formulas, entails that the information required for multivariate polynomial approximation can be suitably compressed. 2000 AMS subject classification: 41A10, 65D32.

متن کامل

A Note on Tchakaloff’s Theorem

A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.

متن کامل

New measures of graph irregularity

In this paper, we tighten the concise Turán theorem for irregular graphs, using spectral and non-spectral proofs. We then investigate to what extent Turán’s theorem can be similarly strengthened for generalized r-partite graphs.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003