{"id":5671,"date":"2023-09-14T17:17:15","date_gmt":"2023-09-14T14:17:15","guid":{"rendered":"https:\/\/iamm.in.ua\/?p=5671"},"modified":"2023-10-11T12:11:17","modified_gmt":"2023-10-11T09:11:17","slug":"seminar-contemporary-analysis-and-partial-differential-equations-29-09-2023","status":"publish","type":"post","link":"https:\/\/iamm.in.ua\/?p=5671&lang=en","title":{"rendered":"SEMINAR \u201cContemporary Analysis and Partial Differential Equations\u201d (29.09.2023)"},"content":{"rendered":"<p><script src=\"https:\/\/polyfill.io\/v3\/polyfill.min.js?features=es6\"><span data-mce-type=\"bookmark\" class=\"mce_SELRES_start\">\ufeff<\/span><\/script><br \/>\n<script id=\"MathJax-script\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-mml-chtml.js\" async=\"\"><\/script><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"size-medium wp-image-4770 alignright\" title=\"\" src=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea-300x84.jpg\" alt=\"\" width=\"300\" height=\"84\" srcset=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea-300x84.jpg 300w, https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea.jpg 483w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-4773 alignleft\" title=\"\" src=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM-300x292.png\" alt=\"\" width=\"133\" height=\"129\" srcset=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM-300x292.png 300w, https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM.png 583w\" sizes=\"(max-width: 133px) 100vw, 133px\" \/><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/scholar.google.com\/citations?hl=en&amp;user=wTFHm98AAAAJ&amp;view_op=list_works&amp;sortby=pubdate\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Ivan Kovalyov<\/span><\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Universit\u00e4t Osnabr\u00fcck, Germany<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">i.m.kovalyov@gmail.com<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong><em>Indefinite Stieltjes Moment Problem and Jacobi Matrices<\/em><\/strong><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Friday, 29 September 2023 at 13:00<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">On line: <a href=\"https:\/\/meet.google.com\/nif-zfwd-mrg\">https:\/\/meet.google.com\/nif-zfwd-mrg<\/a><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong>Abstract<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Let \\(\\mathbf{J}\\) be a monic generalized Jacobi matrix, i.e. a three-diagonal block matrix of a special form, introduced by M. Derevyagin and V. Derkach in 2004. We find conditions for a monic generalized Jacobi matrix \\(\\mathbf{J}\\) to admit a factorization \\(\\mathbf{J} = \\mathbf{L}\\mathbf{U}\\) with \\(\\mathbf{L}\\) and \\(\\mathbf{U}\\) being lower and upper triangular two-diagonal block matrices of a special form. In this case the Darboux transformation of \\(\\mathbf{J}\\) defined by \\(\\mathbf{J}^p = \\mathbf{L}\\mathbf{U}\\) it is shown to be also a monic generalized Jacobi matrix. Analogues of Christoffel formulas for polynomials of the first and the second kind, corresponding to the Darboux transformation \\(\\mathbf{J}^p\\) are found. As was known, the generalized Jacobi matrix is associated with the indefinite Stieltjes moment problem. Hence, we consider one in the class \\(N_{\\kappa}^k\\) of generalized Stieltjes functions. The set of the solution can be described by Schur step-by-step algorithm, which is based on the expansion of the solutions in the generalized Stieltjes continued fraction. The resolvent matrix is represented in terms of generalized Stieltjes polynomials.<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Seminar video report<\/span><\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/SHPl5Rn8mM0\" width=\"560\" height=\"314\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"slide-text-bg2\"><span>&nbsp; &nbsp; &nbsp; &nbsp; Ivan Kovalyov Universit\u00e4t Osnabr\u00fcck, Germany i.m.kovalyov@gmail.com Indefinite Stieltjes Moment Problem and Jacobi Matrices F<\/span><\/div>\n<div class=\"slide-btn-area-sm\"><a href=\"https:\/\/iamm.in.ua\/?p=5671&#038;lang=en\" class=\"slide-btn-sm\">\u041f\u0440\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0435<\/a><\/div>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[99,74],"tags":[],"_links":{"self":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5671"}],"collection":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5671"}],"version-history":[{"count":16,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5671\/revisions"}],"predecessor-version":[{"id":5928,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5671\/revisions\/5928"}],"wp:attachment":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}