{"id":43784,"date":"2026-03-28T07:35:06","date_gmt":"2026-03-28T07:35:06","guid":{"rendered":"https:\/\/www.tugraz-verlag.at\/gesamtverzeichnis\/unkategorisiert\/empty-product-container-19\/"},"modified":"2026-03-28T11:36:07","modified_gmt":"2026-03-28T09:36:07","slug":"approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense","status":"publish","type":"product","link":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/","title":{"rendered":"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense"},"content":{"rendered":"<p>This thesis is devoted to the approximation of Dirac operators with \u03b4-shell potentials by Dirac operators with strongly localized potentials. In particular, for the first time norm-resolvent convergence is considered. In this setting, convergence conditions, counterexamples and important spectral implications are presented.<\/p>","protected":false},"excerpt":{"rendered":"<p>This thesis is devoted to the approximation of Dirac operators with \u03b4-shell potentials by Dirac operators with strongly localized potentials. In particular, for the first time norm-resolvent convergence is considered. In this setting, convergence conditions, counterexamples and important spectral implications are presented.<\/p>\n","protected":false},"featured_media":43838,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false},"product_brand":[],"product_cat":[1630],"product_tag":[3859],"class_list":{"0":"post-43784","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-mathematik-physik-und-geodaesie","7":"product_tag-heat-equation-space-time-methods-boundary-integral-equations-hypersingular-operator-integration-by-parts-formula-boundary-element-methods-fmm-adaptivity-parallelization-hpc","8":"autor-christian-stelzer-landauer","9":"reihe-monographic-series-tu-graz","10":"reihe-monographic-series-tu-grazcomputation-in-engineering-and-science","12":"first","13":"instock","14":"taxable","15":"shipping-taxable","16":"purchasable","17":"product-type-simple"},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense - Verlag der TU Graz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense - Verlag der TU Graz\" \/>\n<meta property=\"og:description\" content=\"This thesis is devoted to the approximation of Dirac operators with \u03b4-shell potentials by Dirac operators with strongly localized potentials. In particular, for the first time norm-resolvent convergence is considered. In this setting, convergence conditions, counterexamples and important spectral implications are presented.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/\" \/>\n<meta property=\"og:site_name\" content=\"Verlag der TU Graz\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-28T09:36:07+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png\" \/>\n\t<meta property=\"og:image:width\" content=\"633\" \/>\n\t<meta property=\"og:image:height\" content=\"930\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/\",\"url\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/\",\"name\":\"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense - Verlag der TU Graz\",\"isPartOf\":{\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.tugraz-verlag.at\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png\",\"datePublished\":\"2026-03-28T07:35:06+00:00\",\"dateModified\":\"2026-03-28T09:36:07+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[[\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/\"]]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#primaryimage\",\"url\":\"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png\",\"contentUrl\":\"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png\",\"width\":633,\"height\":930},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.tugraz-verlag.at\/en\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Gesamtverzeichnis\",\"item\":\"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.tugraz-verlag.at\/en\/#website\",\"url\":\"https:\/\/www.tugraz-verlag.at\/en\/\",\"name\":\"Verlag der TU Graz\",\"description\":\"Verlag der Technischen Universit\u00e4t Graz\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.tugraz-verlag.at\/en\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense - Verlag der TU Graz","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/","og_locale":"en_US","og_type":"article","og_title":"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense - Verlag der TU Graz","og_description":"This thesis is devoted to the approximation of Dirac operators with \u03b4-shell potentials by Dirac operators with strongly localized potentials. In particular, for the first time norm-resolvent convergence is considered. In this setting, convergence conditions, counterexamples and important spectral implications are presented.","og_url":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/","og_site_name":"Verlag der TU Graz","article_modified_time":"2026-03-28T09:36:07+00:00","og_image":[{"width":633,"height":930,"url":"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/","url":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/","name":"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense - Verlag der TU Graz","isPartOf":{"@id":"https:\/\/www.tugraz-verlag.at\/en\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#primaryimage"},"image":{"@id":"https:\/\/www.tugraz-verlag.at\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#primaryimage"},"thumbnailUrl":"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png","datePublished":"2026-03-28T07:35:06+00:00","dateModified":"2026-03-28T09:36:07+00:00","breadcrumb":{"@id":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":[["https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/"]]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#primaryimage","url":"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png","contentUrl":"https:\/\/www.tugraz-verlag.at\/wp-content\/uploads\/asolmerce\/image-cover_stelzer-landauer_ces_47.png","width":633,"height":930},{"@type":"BreadcrumbList","@id":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/mathematik-physik-und-geodaesie\/approximation-of-dirac-operators-with-delta-shell-potentials-in-the-norm-resolvent-sense\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.tugraz-verlag.at\/en\/"},{"@type":"ListItem","position":2,"name":"Gesamtverzeichnis","item":"https:\/\/www.tugraz-verlag.at\/en\/gesamtverzeichnis\/"},{"@type":"ListItem","position":3,"name":"Approximation of Dirac Operators with Delta-shell Potentials in the Norm Resolvent Sense"}]},{"@type":"WebSite","@id":"https:\/\/www.tugraz-verlag.at\/en\/#website","url":"https:\/\/www.tugraz-verlag.at\/en\/","name":"Verlag der TU Graz","description":"Verlag der Technischen Universit\u00e4t Graz","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.tugraz-verlag.at\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/product\/43784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/comments?post=43784"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/media\/43838"}],"wp:attachment":[{"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/media?parent=43784"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/product_brand?post=43784"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/product_cat?post=43784"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/www.tugraz-verlag.at\/en\/wp-json\/wp\/v2\/product_tag?post=43784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}