{"id":43774,"date":"2023-03-29T13:18:30","date_gmt":"2023-03-29T09:18:30","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?p=43774"},"modified":"2023-03-30T18:48:37","modified_gmt":"2023-03-30T14:48:37","slug":"f-r-e-d-bil%c9%99nd%c9%99r-pasa-oglu-allahverdiyev-hilbert-f%c9%99zalarinda-oz-ozun%c9%99-qosma-v%c9%99-oz-ozun%c9%99-qosma-olmayan-operatorlarin-spektral-n%c9%99z%c9%99riyy%c9%99sinin-2","status":"publish","type":"post","link":"https:\/\/www.imm.az\/exp\/2023\/03\/29\/f-r-e-d-bil%c9%99nd%c9%99r-pasa-oglu-allahverdiyev-hilbert-f%c9%99zalarinda-oz-ozun%c9%99-qosma-v%c9%99-oz-ozun%c9%99-qosma-olmayan-operatorlarin-spektral-n%c9%99z%c9%99riyy%c9%99sinin-2\/","title":{"rendered":"F.-r.e.d. Bil\u0259nd\u0259r Pa\u015fa o\u011flu Allahverdiyev\u00a0\u201cHilbert f\u0259zalar\u0131nda \u00f6z-\u00f6zun\u0259 qo\u015fma v\u0259 \u00f6z-\u00f6z\u00fcn\u0259 qo\u015fma olmayan operatorlar\u0131n spektral n\u0259z\u0259riyy\u0259sinin b\u0259zi m\u0259s\u0259l\u0259l\u0259ri\u201d\u00a0m\u00f6vzusunda m\u0259ruz\u0259 edib"},"content":{"rendered":"<p>Bu g\u00fcn AMEA-n\u0131n Riyaziyyat v\u0259 Mexanika \u0130nstitutunda n\u00f6vb\u0259ti \u00dcmuminstitut seminar\u0131 ke\u00e7irilib. \u00dcmuminstitut f.-r.e.d. Bil\u0259nd\u0259r Pa\u015fa o\u011flu Allahverdiyev\u00a0<strong>\u201c<\/strong><strong>Hilbert f\u0259zalar\u0131nda \u00f6z-\u00f6zun\u0259 qo\u015fma v\u0259 \u00f6z-\u00f6z\u00fcn\u0259 qo\u015fma olmayan operatorlar\u0131n spektral n\u0259z\u0259riyy\u0259sinin b\u0259zi m\u0259s\u0259l\u0259l\u0259ri<\/strong><strong>\u201d\u00a0<\/strong>m\u00f6vzusunda m\u0259ruz\u0259 edib.<\/p>\n<p>Hilbert f\u0259zalar\u0131nda t\u0259sir ed\u0259n k\u0259silm\u0259z spektr\u0259 malik \u00f6z-\u00f6z\u00fcne qo\u015fma olmayan operatorlar\u0131n v\u0259 operator qiym\u0259tli funksiyalar\u0131n spektral n\u0259z\u0259riyy\u0259sinin b\u0259zi m\u0259s\u0259l\u0259l\u0259ri t\u0259dqiq edilmi\u015fdir. Simmetrik \u015eredinqer, sinqulyar \u015eturm-Liuvill, Dirak tip (Hamiltonian) v\u0259 f\u0259rq operatorlar\u0131n\u0131n (sonsuz Yakobi matrisl\u0259ri, diskret \u015eturm-Liuvill ve diskret Dirak tip (Hamiltonian) operatorlar) \u00f6z-\u00f6z\u00fcn\u0259 qo\u015fma olan v\u0259 \u00f6z-\u00f6z\u00fcn\u0259 qo\u015fma olmayan (maksimal dissipativ, akkumulyativ) geni\u015fl\u0259nm\u0259l\u0259ri s\u0259rh\u0259d \u015f\u0259rtl\u0259ri vasit\u0259siyl\u0259 tap\u0131lm\u0131\u015fd\u0131r. Bu operatorlar\u0131n maksimal dissipativ geni\u015fl\u0259nm\u0259l\u0259rinin \u00f6z-\u00f6z\u00fcn\u0259 qo\u015fma dilatasiyalar\u0131, dilatasiyalar\u0131n s\u0259pilm\u0259 n\u0259z\u0259riyy\u0259sinin s\u0259pilm\u0259 matrisl\u0259ri qurulmu\u015f v\u0259 maksimal dissipativ operatorlar\u0131n funksional modell\u0259ri\u00a0 qurularaq xarakteristik funksiyalar\u0131 tap\u0131lm\u0131\u015fd\u0131r. Bu operatorlar \u00fc\u00e7\u00fcn m\u0259xsusi v\u0259 qo\u015fulmu\u015f vektorlar\u0131n taml\u0131q m\u0259s\u0259l\u0259l\u0259ri h\u0259ll edilmi\u015fdir. Bu m\u0259s\u0259l\u0259l\u0259r s\u0259rh\u0259d \u015f\u0259rtl\u0259rind\u0259 spektral parametr olan sinqulyar \u015eturm-Liuvill, Dirak tip (Hamiltonian), f\u0259rq operatorlar\u0131 v\u0259 matris \u0259msall\u0131 \u015eredinqer, sinqulyar \u015eturm-Liuvill, Dirak tip (Hamiltonian) v\u0259 f\u0259rq operatorlar\u0131 (sonsuz Yakobi matrisl\u0259ri, diskret \u015eturm-Liuvill ve diskret Dirak tip (Hamiltonian) operatorlar) \u00fc\u00e7\u00fcn d\u0259 h\u0259ll edilmi\u015fdir.\u00a0 \u0130mpulsiv sinqulyar \u015eturm-Liuvill v\u0259 Dirak tip (Hamiltonian) sistemler \u00fc\u00e7\u00fcn spektral analizin b\u0259zi m\u0259s\u0259l\u0259l\u0259ri h\u0259ll edilmi\u015fdir. Zaman \u015fkalas\u0131nda bax\u0131lan \u015eturm-Liuvill ve Dirak operatorlar\u0131n\u0131n spektral xass\u0259l\u0259ri ara\u015fd\u0131r\u0131lm\u0131\u015fd\u0131r. Requlyar v\u0259 singulyar q-\u015eturm-Liuvill, q-Dirak, q-Hamiltonian, Hahn-\u015eturm-Liuvill, Hahn-Dirak, Hahn-Hamiltonian sisteml\u0259r \u00fc\u00e7\u00fcn spektral n\u0259z\u0259riyy\u0259nin bir \u00e7ox m\u0259s\u0259l\u0259l\u0259ri h\u0259ll edilmi\u015fdir. B\u0259zi diferensial ve q-f\u0259rq operatorlar\u0131n\u0131n m\u0259xsusi v\u0259 qo\u015fulmu\u015f vektorlar\u0131n\u0131n Riss ve Bari bazislik m\u0259s\u0259l\u0259l\u0259ri h\u0259ll edilmi\u015fdir. Qeyri-x\u0259tti sinqulyar \u015eturm-Liuvill, q-\u015eturm-Liuvill, Hahn-\u015eturm-Liuvill m\u0259s\u0259l\u0259l\u0259rinin varl\u0131q ve yegan\u0259lik teoremleri isbat edilmi\u015fdir.<\/p>\n<div class='entry-gallery'><div id=\"carousel-1\" class=\"single-carousel carousel slide carousel-43774\" data-ride=\"carousel\"><ol class='carousel-indicators'><li data-target=\"#carousel-1\" data-slide-to=\"0\" class=\"active\"><\/li><li data-target=\"#carousel-1\" data-slide-to=\"1\" class=\"\"><\/li><li data-target=\"#carousel-1\" data-slide-to=\"2\" class=\"\"><\/li><li data-target=\"#carousel-1\" data-slide-to=\"3\" class=\"\"><\/li><\/ol><div class='carousel-inner'><div class=\"carousel-item item active\"><a 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X\u0259b\u0259rl\u0259rd\u0259n istifad\u0259 ed\u0259rk\u0259n www.imm.az sayt\u0131na istinad z\u0259ruridir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu g\u00fcn AMEA-n\u0131n Riyaziyyat v\u0259 Mexanika \u0130nstitutunda n\u00f6vb\u0259ti \u00dcmuminstitut seminar\u0131 ke\u00e7irilib. \u00dcmuminstitut f.-r.e.d. Bil\u0259nd\u0259r Pa\u015fa o\u011flu Allahverdiyev\u00a0\u201cHilbert f\u0259zalar\u0131nda \u00f6z-\u00f6zun\u0259 qo\u015fma v\u0259 \u00f6z-\u00f6z\u00fcn\u0259 qo\u015fma olmayan operatorlar\u0131n spektral n\u0259z\u0259riyy\u0259sinin b\u0259zi m\u0259s\u0259l\u0259l\u0259ri\u201d\u00a0m\u00f6vzusunda m\u0259ruz\u0259 edib. Hilbert f\u0259zalar\u0131nda t\u0259sir ed\u0259n k\u0259silm\u0259z spektr\u0259 malik \u00f6z-\u00f6z\u00fcne qo\u015fma olmayan operatorlar\u0131n v\u0259 operator qiym\u0259tli funksiyalar\u0131n spektral n\u0259z\u0259riyy\u0259sinin b\u0259zi m\u0259s\u0259l\u0259l\u0259ri t\u0259dqiq edilmi\u015fdir. Simmetrik \u015eredinqer, sinqulyar [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":43816,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[77],"tags":[],"_links":{"self":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/43774"}],"collection":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/comments?post=43774"}],"version-history":[{"count":3,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/43774\/revisions"}],"predecessor-version":[{"id":43818,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/43774\/revisions\/43818"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/media\/43816"}],"wp:attachment":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/media?parent=43774"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/categories?post=43774"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/tags?post=43774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}