DILATION VOLUMES OF SETS OF FINITE PERIMETER

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385931" target="_blank" >RIV/00216208:11320/18:10385931 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/apr.2018.52" target="_blank" >https://doi.org/10.1017/apr.2018.52</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/apr.2018.52" target="_blank" >10.1017/apr.2018.52</a>

Result language
angličtina
Original language name
DILATION VOLUMES OF SETS OF FINITE PERIMETER
Original language description
In this paper we analyze the first-order behavior (that is, the right-sided derivative) of the volume of the dilation A circle plus t Q as t converges to 0. Here A and Q are subsets of n-dimensional Euclidean space, A has finite perimeter, and Q is finite. If Q consists of two points only, x and x + u, say, this derivative coincides up to a sign with the directional derivative of the covariogram of A in direction u. By known results for the covariogram, this derivative can therefore be expressed by the cosine transform of the surface area measure of A. We extend this result to finite sets Q and use it to determine the derivative of the contact distribution function with finite structuring element of a stationary random set at 0. The proofs are based on an approximation of the indicator function of A by smooth functions of bounded variation.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)