<p>We study the expansions of the elements in <em>S</em>(ℝ<sub>+</sub><sup>d</sup>) and <em>S</em>'(ℝ<sub>+</sub><sup>d</sup>) with respect to the Laguerre orthonormal basis. As a consequence, we obtain the Schwartz kernel theorem for <em>S</em>(ℝ<sub>+</sub><sup>d</sup>) and <em>S</em>'(ℝ<sub>+</sub><sup>d</sup>). Also we give the extension theorem of Whitney type for <em>S</em>(ℝ<sub>+</sub><sup>d</sup>). Next, we consider the G-type spaces i.e. the spaces <em>G</em><sub><em>α</em></sub><sup><em>α</em></sup>(ℝ<sub>+</sub><sup>d</sup>), α≥1 and their dual spaces which can be described as analogous to the Gelfand-Shilov spaces and their dual spaces. Actually, we show the exist-ence of the topological isomorphism between the <em>G</em>-type spaces and the subspaces of the Gelfand-Shilov spaces <em>S</em><sub>α/2</sub><sup>α/2</sup>(ℝ<sup>d</sup>), α≥1 consisting of "even" functions. Next, we show that the Fourier Laguerre coecients of the elements in the <em>G</em>-type spaces and their dual spaces characterize these spaces through the exponential and sub-exponentia l growth of the coecients. We provide the full topological description and the kernel theorem is proved. Also two structural theorems for the dual spaces of <em>G</em>-type spaces are obtained. Furthemore, we dene the new class of the Weyl pseudo-dierential operators with radial symbols belonging to the G-type spaces and their dual spaces. The continuity properties of this class of pseudo-dierential operators over the Gelfand-Shilov type spaces and their duals are proved. In this way the class of the Weyl pseudo-dierential operators is extended to the one with the radial symbols with the exponential and sub-exponential growth rate.</p> / <p>Proučavamo razvoje elemenata iz <em>S</em>(ℝ<sub>+</sub><sup>d</sup>) i <em>S</em>'(ℝ<sub>+</sub><sup>d</sup>) preko Lagerove ortonormirane baze. Kao posledicu dobijamo Švarcovu teoremu o jezgru za preko Lagerove ortonormirane baze. Kao posledicu dobijamo Švarcovu teoremu o jezgru za <em>S</em>(ℝ<sub>+</sub><sup>d</sup>) i <em>S</em>'(ℝ<sub>+</sub><sup>d</sup>). Takođe, pokazujemo i Teoremu Vitnijevog tipa za <em>S</em>(ℝ<sub>+</sub><sup>d</sup>) . Zatim, posmatramo prostore G-tipa i.e. prostore <em>G</em><sub>α</sub><sup>α</sup>(ℝ<sup>d</sup>), α ≥ 1 i njihove duale koji su analogni sa Geljfand-Šilovim prostorima i njihovim dualima. Zapravo, pokazujemo da postoji topološki izomorfizam između prostora <em>G</em>-tipa i potprostora Geljfand-Šilovih prostora <em>S</em><sub>α/2</sub><sup>α/2</sup>(ℝ<sup>d</sup>), α ≥ 1 koji sadrže "parne" funkcije. Dalje, dokazujemo da Furije Lagerovi koeficijenti elemenata iz prostora <em>G</em>-tipa i njihovih duala karakterišu ove prostore kroz eksponencijalni i sub-eksponencijalni rast tih koeficijenata. Opisujemo topološku strukturu ovih prostora i dajemo Švarcovu teoremu o jezgru. Takođe, dve strukturalne teoreme za duale prostora <em>G</em>-tipa su dobijene. Dalje, definišemo novu klasu Vejlovih pseudo-diferencijalnih operatora sa radijalnim simbolima koji se nalaze u prostorima <em>G</em>-tipa i njihovim dualima. Pokazana je neprekidnost ove klase Vejlovih pseudo-diferencijalnih operatora na prostorima Geljfand-Šilova i na njihovim dualima. Na ovaj način klasa Vejlovih pseudo-diferencijalnih operatora je proširena na radijalne simbole koji imaju eksponencijalni i sub-eksponencijalni rast.</p>
| Identifer | oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)101443 |
| Date | 28 September 2016 |
| Creators | Jakšić Smiljana |
| Contributors | Pilipović Stevan, Prangoski Bojan, Teofanov Nenad, Seleši Dora, Mitrović Slobodanka |
| 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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