|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
On H.Weyl and J.Steiner polynomials | | Victor Katsnelson
; | | Date: |
16 Mar 2008 | | Abstract: | The paper deals with root problems for two classes of univariate polynomials
both of geometric origin.
The first class discussed, the class of Steiner polynomial, consists of
polynomials, each associated with a compact convex set V in R^n. A polynomial
of this class describes the volume of the set V+tB^n as a function of t, where
t is a positive number and B^n denotes the unit ball in R. The second class,
the class of Weyl polynomials, consists of polynomials, each associated with a
Riemannian manifold M, where M} is isometrically embedded with positive
codimension in R^n. A Weyl polynomial describes the volume of a tubular
neighborhood of its associated M as a function of the tube’s radius. These
polynomials are calculated explicitly in a number of natural examples such as
balls, cubes, squeezed cylinders. Furthermore, we examine how the above
mentioned polynomials are related to one another and how they depend on the
standard embedding of R^n into R^m for m>n. We find that in some cases the real
part of any Steiner polynomial root will be negative. In certain other cases, a
Steiner polynomial will have only real negative roots. In all of this cases, it
can be shown that all of a Weyl polynomial’s roots are simple and, furthermore,
that they lie on the imaginary axis. At the same time, in certain cases the
above pattern does not hold. | | Source: | arXiv, 0803.2346 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER