CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt144",{id:"formSmash:upper:j_idt144",widgetVar:"widget_formSmash_upper_j_idt144",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt145_j_idt147",{id:"formSmash:upper:j_idt145:j_idt147",widgetVar:"widget_formSmash_upper_j_idt145_j_idt147",target:"formSmash:upper:j_idt145:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Discrepancy densities for planar and hyperbolic zero packingPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2017 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 272, no 12, p. 5282-5306Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

ACADEMIC PRESS INC ELSEVIER SCIENCE , 2017. Vol. 272, no 12, p. 5282-5306
##### Keyword [en]

Geometric zero packing, (partial derivative)over-bar-Estimates, Asymptotic variance
##### National Category

Mathematical Analysis
##### Identifiers

URN: urn:nbn:se:kth:diva-207866DOI: 10.1016/j.jfa.2017.01.022ISI: 000400539700013Scopus ID: 2-s2.0-85012936428OAI: oai:DiVA.org:kth-207866DiVA, id: diva2:1102896
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt473",{id:"formSmash:j_idt473",widgetVar:"widget_formSmash_j_idt473",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt479",{id:"formSmash:j_idt479",widgetVar:"widget_formSmash_j_idt479",multiple:true});
##### Note

##### In thesis

We study the problem of geometric zero packing, recently introduced by Hedenmalrn [7]. There are two natural densities associated with this problem: the discrepancy density pa, given by rho(H) = lim (r -> 1-) inf inf(f) integral(D(0,r)) ((1 - vertical bar z vertical bar(2)) vertical bar f(z)vertical bar - 1)(2) dA(z)/1 - vertical bar z vertical bar(2)/ integral(D(0,r)) dA(z)/1 - vertical bar z vertical bar(2) which measures the discrepancy in optimal approximation of (1 - vertical bar z vertical bar(2))(-1) with the modulus of polynomials f, and its relative, the tight discrepancy density rho*(H), which will trivially satisfy pH < per. These densities have deep connections to the boundary behaviour of conformal mappings with k-quasiconformal extensions, which can be seen from Hedenmalm's result that the universal asymptotic variance Sigma(2) is related to rho(H)* by Sigma(2) = 1 - rho(H)* . Here we prove that in fact rho(H) = rho(H)*, resolving a conjecture by Hedenmalm in the positive. The natural planar analogues rho(C) and rho(C)* to these densities make contact with work of Abrikosov on Bose Einstein condensates. As a second result we prove that also rho(C) = rho(C)*. The methods are based on Ameur, Hedenmalm and Makarov's Hormander-type <(partial derivative)over bar>-estimates with polynomial growth control [2]. As a consequence we obtain sufficiency results on the degrees of approximately optimal polynomials.

QC 20170530

Available from: 2017-05-30 Created: 2017-05-30 Last updated: 2018-05-17Bibliographically approved1. Random and optimal configurations in complex function theory$(function(){PrimeFaces.cw("OverlayPanel","overlay1206742",{id:"formSmash:j_idt787:0:j_idt791",widgetVar:"overlay1206742",target:"formSmash:j_idt787:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1256",{id:"formSmash:j_idt1256",widgetVar:"widget_formSmash_j_idt1256",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1309",{id:"formSmash:lower:j_idt1309",widgetVar:"widget_formSmash_lower_j_idt1309",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1310_j_idt1312",{id:"formSmash:lower:j_idt1310:j_idt1312",widgetVar:"widget_formSmash_lower_j_idt1310_j_idt1312",target:"formSmash:lower:j_idt1310:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});