{"id":25360,"date":"2021-10-14T13:07:08","date_gmt":"2021-10-14T11:07:08","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25360"},"modified":"2022-01-14T13:08:47","modified_gmt":"2022-01-14T12:08:47","slug":"ferrando-j-c-2021-a-dirac-delta-operator-mathematics-and-statistics-9-2179-187-2","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2021\/10\/14\/ferrando-j-c-2021-a-dirac-delta-operator-mathematics-and-statistics-9-2179-187-2\/","title":{"rendered":"Ferrando, J.C. (2021) \u00abA dirac delta operator\u00bb, Mathematics and Statistics, 9 (2):179\u2013187"},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong style=\"font-size: 18px\">Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>If T is a (densely defined) self-adjoint operator acting on a complex Hilbert space H and I stands for the identity operator, we introduce the delta function operator \u03bb {mapping} \u03b4 (\u03bbI &#8211; T) at T. When T is a bounded operator, then \u03b4 (\u03bbI &#8211; T) is an operator-valued distribution. If T is unbounded, \u03b4 (\u03bbI &#8211; T) is a more general object that still retains some properties of distributions. We provide an explicit representation of \u03b4 (\u03bbI &#8211; T) in some particular cases, derive various operative formulas involving \u03b4 (\u03bbI &#8211; T) and give several applications of its usage in Spectral Theory as well as in Quantum Mechanics.<\/p>","protected":false},"excerpt":{"rendered":"<p>Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)<br \/>\nAbstract: If T is a (densely defined) self-adjoint operator acting on a complex Hilbert space H and I stands for the identity operator, we introduce the delta function operator \u03bb {mapping} \u03b4 (\u03bbI &#8211; T) at T. When T is a bounded operator, then \u03b4 [&#8230;]<\/p>","protected":false},"author":5675,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25360"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/5675"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=25360"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25360\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}