{"id":896,"date":"2018-03-06T09:20:59","date_gmt":"2018-03-06T08:20:59","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/znanost\/?p=896"},"modified":"2020-02-18T14:31:04","modified_gmt":"2020-02-18T13:31:04","slug":"funkcionalna-analiza","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/znanost\/funkcionalna-analiza\/","title":{"rendered":"Funkcionalna analiza"},"content":{"rendered":"<div class=\"wpb-content-wrapper\">[vc_row][vc_column width=&#8221;1\/4&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]<strong>Odjel\/Katedra: <\/strong><br \/>\nOdjel za matematiku[\/mk_title_box][mk_employees column=&#8221;1&#8243; custom_image_size=&#8221;true&#8221; image_size=&#8221;medium&#8221; rounded_image=&#8221;false&#8221; grayscale_image=&#8221;false&#8221; employees=&#8221;18765&#8243;][\/vc_column][vc_column width=&#8221;3\/4&#8243;][vc_column_text css=&#8221;.vc_custom_1520324357131{margin-bottom: 0px !important;}&#8221;]\n<h4>Podru\u010dje istra\u017eivanja:<\/h4>\n<p>Teorija vali\u0107a (Parsevalovi i ortonormirani vali\u0107i, postupci konstrukcije odre\u0111enih klasa vali\u0107a, skaliraju\u0107e funkcije, multirezolucijska analiza, karakteristi\u010dna matrica)[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520324388388{margin-bottom: 0px !important;}&#8221;]\n<h4>Opis istra\u017eivanja:<\/h4>\n<p>Prou\u010davaju se ortonormirani i Parsevalovi vali\u0107i i multivali\u0107i u n-dimenzionalnom prostoru. Rezolucijski nivoi su definirani proizvoljnom ekspanzivnom matricom s cjelobrojnim koeficijentima. Osmi\u0161ljena je metoda konstrukcije takvih vali\u0107a primjenom tehnike generalizirane multirezolucijske analize (GMRA). Korjenski potprostor prile\u017ee\u0107e GMRA je proizvoljan translaciono invarijantan potprostor \u0161to zna\u010di da nema restrikcija na broj njegovih generatora. Konstruirana je prikladna visokopropusna filtarska matrica koja predstavlja poop\u0107enje dobro poznatog koncepta visokopropusnog filtra iz klasi\u010dne teorije MRA vali\u0107a s dijadskim dilatacijama na realnom pravcu. Metoda je prezentirana na nekoliko primjera a razmatra se i \u0161ira skupina novih primjera. Analiziraju se dobiveni rezultati i poku\u0161ava se dobiti op\u0107i opis nekih klasa vali\u0107a i s njima vezanih multirezolucijskih struktura.[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520324418165{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Kontakti s akademskim i drugim institucijama:<\/strong><\/h4>\n<p>&#8211; PMF \u2013 Matemati\u010dki odsjek, Zagreb<br \/>\n[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520324440797{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Planovi budu\u0107ih istra\u017eivanja:<\/strong><\/h4>\n<p>Planiraju se odre\u0111ena pobolj\u0161anja opisane konstrukcije i novi primjeri. Tako\u0111er postoji i niz pitanja o me\u0111usobnoj povezanosti razli\u010ditih klasa multivali\u0107a i njihovim karakteristikama (primjerice dimenzijska funkcija) na koja \u0107e se poku\u0161ati odgovoriti.[\/vc_column_text][\/vc_column][\/vc_row]\n<\/div>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column width=&#8221;1\/4&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]Odjel\/Katedra: Odjel za matematiku[\/mk_title_box][mk_employees column=&#8221;1&#8243; custom_image_size=&#8221;true&#8221; image_size=&#8221;medium&#8221; rounded_image=&#8221;false&#8221; grayscale_image=&#8221;false&#8221; employees=&#8221;18765&#8243;][\/vc_column][vc_column width=&#8221;3\/4&#8243;][vc_column_text css=&#8221;.vc_custom_1520324357131{margin-bottom: 0px !important;}&#8221;] Podru\u010dje istra\u017eivanja: Teorija vali\u0107a (Parsevalovi i ortonormirani vali\u0107i, postupci konstrukcije odre\u0111enih klasa vali\u0107a, skaliraju\u0107e funkcije, multirezolucijska analiza, karakteristi\u010dna matrica)[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520324388388{margin-bottom: 0px !important;}&#8221;] Opis istra\u017eivanja: Prou\u010davaju se ortonormirani i Parsevalovi vali\u0107i i multivali\u0107i u n-dimenzionalnom prostoru. Rezolucijski nivoi su [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":903,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[11,26],"tags":[],"poredak":[],"class_list":["post-896","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-odjel-za-matematiku","category-samostalna-istrazivanja"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Funkcionalna analiza - Znanstvena djelatnost, PMF Split<\/title>\n<meta name=\"robots\" content=\"noindex, follow\" \/>\n<meta property=\"og:locale\" content=\"hr_HR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Funkcionalna analiza - Znanstvena djelatnost, PMF Split\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column width=&#8221;1\/4&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]Odjel\/Katedra: Odjel za matematiku[\/mk_title_box][mk_employees column=&#8221;1&#8243; custom_image_size=&#8221;true&#8221; image_size=&#8221;medium&#8221; rounded_image=&#8221;false&#8221; grayscale_image=&#8221;false&#8221; employees=&#8221;18765&#8243;][\/vc_column][vc_column width=&#8221;3\/4&#8243;][vc_column_text css=&#8221;.vc_custom_1520324357131{margin-bottom: 0px !important;}&#8221;] Podru\u010dje istra\u017eivanja: Teorija vali\u0107a (Parsevalovi i ortonormirani vali\u0107i, postupci konstrukcije odre\u0111enih klasa vali\u0107a, skaliraju\u0107e funkcije, multirezolucijska analiza, karakteristi\u010dna matrica)[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520324388388{margin-bottom: 0px !important;}&#8221;] Opis istra\u017eivanja: Prou\u010davaju se ortonormirani i Parsevalovi vali\u0107i i multivali\u0107i u n-dimenzionalnom prostoru. 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