{"id":72,"date":"2018-11-09T11:46:00","date_gmt":"2018-11-09T13:46:00","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=72"},"modified":"2019-04-11T11:48:53","modified_gmt":"2019-04-11T14:48:53","slug":"a-new-geometric-viewpoint-on-sturm-liouville-eigenvalue-problems","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/a-new-geometric-viewpoint-on-sturm-liouville-eigenvalue-problems\/","title":{"rendered":"A new geometric view on Sturm-Liouville eigenvalue problems"},"content":{"rendered":"<p id=\"h.p_PQ0X8ogC99iA\" class=\"zfr3Q\">V. Balestro, H. Martini and R. Teixeira, <strong>A new geometric view on Sturm-Liouville eigenvalue problems<\/strong>, to appear in Monatsh. Math., 2018. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1809.02975&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNEOn3FA_GnlcFZFOrsRLvhEby1XOQ\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>) (<a href=\"https:\/\/link.springer.com\/article\/10.1007%2Fs00605-019-01291-9\">journal link)<\/a><\/p>\n<p id=\"h.p_OY9Otf7q-NzN\" class=\"zfr3Q\">Comments: In this paper we investigate further the relation of certain Sturm-Liouville equations with geometries given by norms in a plane. We prove that whenever the equation is related to a certain geometry, then any affinely equivalent geometry is associated to this same equation. We also show that, in the particular case of Radon planes, the solutions of the associated Sturm-Liouville eigenvalue problem are given by trigonometric functions (as in the Euclidean case). Further, we study the conditions under which a given Sturm-Liouville problem yields a norm, proving that this occurs precisely when the first positive eigenvalue is double and equals 1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro, H. Martini and R. Teixeira, A new geometric view on Sturm-Liouville eigenvalue problems, to appear in Monatsh. Math., 2018. (arXiv link) (journal link) Comments: In this paper we investigate further the relation of certain Sturm-Liouville equations with geometries given by norms in a plane. We prove that whenever the equation is related to [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-72","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/72","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/users\/205"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/comments?post=72"}],"version-history":[{"count":2,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/72\/revisions"}],"predecessor-version":[{"id":231,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/72\/revisions\/231"}],"up":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=72"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=72"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=72"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}