DILATION VOLUMES OF SETS OF FINITE PERIMETER

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

DILATION VOLUMES OF SETS OF FINITE PERIMETER

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

DILATION VOLUMES OF SETS OF FINITE PERIMETER

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA15-08218S" target="_blank" >GA15-08218S: Teorie reálných funkcí a její aplikace v geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Applied Probability

ISSN

0001-8678

e-ISSN

—

Svazek periodika

50

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

24

Strana od-do

1095-1118

Kód UT WoS článku

000451616400004

EID výsledku v databázi Scopus

2-s2.0-85057816133