<p>We introduce a family of smooth functions which are "less regu-lar" than the Gevrey functions, and study its basic properties. In particular we prove the standard results concerning algebra property and stability under finite order derivation. Moreover, we construct infnite order operators which leads us to the definition of class with ultradifferentiable property. We also prove that our classes are inverse-closed, and this result is the essential part in the proof of our main result presented in the final Chapter. Moreover, using the techniques of microlocal analysis, we introduce and investigate the<br />corresponding wave front sets, and the prove the results related to singular support of a distribution. Our main results shows how the singularities of solutions to partial differential equations (PDE's in short) propagate in the framework of our regularity.</p> / <p>U ovoj tezi definišemo novu klasu glatkih funkcija i izučavamo njihove osnovne osobine. Pokazujemo da naše klase imaju svojsto algebre kao i da su zatvorene u odnosu na delovanje operatora izvoda konačnog reda.Sta više, konstruišemo diferencijalne operatore beskonačnog reda i to nas dovodi do definicije ultradiferencijabilnih klasa funkcija. Takode dokazujemo osobinu zatvorenosti u odnosu na inverze, i taj rezultat je najvažniji deo u dokazu glavne teoreme koja je formulisana u poslednjoj glavi. Koristeći tehnike mikrolokalne analize, uvodimo i izučavamo odgovarajuće talasne frontove, i pokazujemo odgovarajuća tvrdjenja vezana za singularni nosač distribucije. Naš glavni rezultat pokazuje kako se prostiru singulariteti rešenja linearnih parcijalnih diferencijalnih jednačina u okviru naše regularnosti.</p>
| Identifer | oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)101444 |
| Date | 30 September 2016 |
| Creators | Tomić Filip |
| Contributors | Teofanov Nenad, Pilipović Stevan, Prangoski Bojan |
| Publisher | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, University of Novi Sad, Faculty of Sciences at Novi Sad |
| Source Sets | University of Novi Sad |
| Language | English |
| Detected Language | English |
| Type | PhD thesis |
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