{"id":791,"date":"2026-05-04T14:21:18","date_gmt":"2026-05-04T14:21:18","guid":{"rendered":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/petrova-veta-a-harmonicka-analyza-mnohouhelniku-petrs-theorem-and-harmonic-analysis-of-polygons-plenary-lecture\/"},"modified":"2026-05-04T14:21:18","modified_gmt":"2026-05-04T14:21:18","slug":"petrova-veta-a-harmonicka-analyza-mnohouhelniku-petrs-theorem-and-harmonic-analysis-of-polygons-plenary-lecture","status":"publish","type":"post","link":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/en\/petrova-veta-a-harmonicka-analyza-mnohouhelniku-petrs-theorem-and-harmonic-analysis-of-polygons-plenary-lecture\/","title":{"rendered":"Petrova v\u011bta a harmonick\u00e1 anal\u00fdza mnoho\u00faheln\u00edk\u016f \u2013 Petr&#039;s theorem and harmonic analysis of polygons (plenary lecture)"},"content":{"rendered":"<p><em>Pavel Pech<\/em><br \/><small>University of South Bohemia, Faculty of Education, \u010cesk\u00e9 Bud\u011bjovice<\/small><\/p>\n<p>Over 120 years have elapsed since K. Petr, the professor of Charles\u2019s university in Prague, established a theorem which is called after him Petr\u2019s theorem. So, it is a good occasion to remind some results which are connected with this theorem.<br \/>\nFirst, plane dosed polygons are harmonically analyzed, i.e. they are expressed in the form of the sum of fundamental k-regular polygons. Using this harmonic analysis the Petr\u2019s theorem is studied.<br \/>\nThen we will investigate plane linear polygon transformations. We will study two kinds of transformations \u2013 S-transformation which is described by means of complex numbers and preserves similarity and A-transformation which is defined by real numbers and is invariant under any affinity.<br \/>\nIn the next part, we use A-transformations to generalization of linear polygon transformations into a space which leads to a space analog of harmonic analysis of polygons.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pavel PechUniversity of South Bohemia, Faculty of Education, \u010cesk\u00e9 Bud\u011bjovice Over 120 years have elapsed since K. Petr, the professor of Charles\u2019s university in Prague, established a theorem which is called after him Petr\u2019s theorem. So, it is a good occasion to remind some results which are connected with this theorem. First, plane dosed polygons [&hellip;]<\/p>\n","protected":false},"author":14,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-791","post","type-post","status-publish","format-standard","hentry","category-presentations"],"_links":{"self":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/791","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/users\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/comments?post=791"}],"version-history":[{"count":0,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/791\/revisions"}],"wp:attachment":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/media?parent=791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/categories?post=791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/tags?post=791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}