On a class of Sturm‐Liouville operators which are connected to PT symmetric problems. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Azizov, Tomas Ya.; Trunk, Carsten
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 991
• Page End: 992
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410476
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>A prominent class of <inline-formula><alternatives><tex-math notation="tex"><![CDATA[$\cal PT$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgh2xqgcn30" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /></alternatives></inline-formula> ‐symmetric Hamiltonians is <disp-formula content-type="mathematics" id="di-ueqn-2"><alternatives><graphic position="anchor" mimetype="image" xlink:href="ark:/27927/pgh2xqgcn53" orientation="portrait" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math notation="TeX"><![CDATA[$H := {1\over2} p^2 + x^2(ix)^N, \quad {\rm for\ } x\in\Gamma$]]></tex-math></alternatives></disp-formula> for some nonnegative number <italic>N</italic>. The associated eigenvalue problem is defined on a contour Γ in a specific area in the complex plane (Stokes wedges), see [3, 5]. In this short note we consider the case <italic>N</italic>=2 only. Here we elaborate the relationship between Stokes lines and Stokes wedges and well‐known limit point/limit circle criteria from [6, 10, 11]. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>