Abstract
Are the notions and results presented in the previous two chapters valid in the multivariate case? The answer is mostly yes, but with some limitations. The notion of Gram matrix is related directly only to sum-of-squares polynomials. Unlike the univariate case, multivariate nonnegative polynomials are not necessarily sum-of-squares. However, positive trigonometric polynomials are sum-of-squares, but the degrees of the sum-of-squares factors may be arbitrarily high, at least theoretically.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Dumitrescu, B. (2007). MULTIVARIATE POLYNOMIALS. In: Positive Trigonometric Polynomials and Signal Processing Applications. Signals and Communication Technology. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5125-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4020-5125-8_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5124-1
Online ISBN: 978-1-4020-5125-8
eBook Packages: EngineeringEngineering (R0)