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On some classes of multipliers and semigroups in the spaces of ultradistributions and hyperfunctions

O nekim klasama multiplikatora i semigrupana prostorima ultradistribucija i hiperfunkcija

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2014
Disertacija.pdf (802.8Kb)
IzvestajKomisije.pdf (194.3Kb)
Author
Velinov, Daniel
Mentor
Pilipović, Stevan
Committee members
Nedeljkov, Marko
Pilipović, Stevan
Teofanov, Nenad
Perišić, Dušanka
Kostić, Marko
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Abstract
We are study the spaces of convolutors and multipliers in the spaces of tempered ultradistributions. There given theorems which gives us the characteri-zation of all the elements which belongs to spaces of convolutors and multipliers. Structural theorem for ultradistribution semigroups and exponential ultradistri-bution semigroups is given. Fourier hyperfunction semigroups and hyperfunction semigroups with non-densely dened generators are analyzed and also structural theorems and spectral characterizations give necessary and sucient conditions for the existence of such semigroups generated by a closed not necessarily densely dened operator A. The abstract Cauchy problem is considered in the Banach valued weighted Beurling ultradistribution setting and given some applications on particular equations.
U disertaciji se proučavaju prostor konvolutora i multiplikatora na prostorima temperiranih ultradistribucija. Dokazane su teoreme koji karakterišu elemente prostora konvolutora i multiplikatora. Date su strukturne teoreme za ultradistribucione  polugrupe i eksponenecijalne polugrupe. Furijeve huperfunkciske polugrupe i hiperfunkciske polugrupe sa generatorima koji su negusto definisani  su analizirani, takođe su date strukturne teoreme i spektralne karakterizacije kao i dovoljni uslovi za postojenje na takvih polugrupa za operator A koji ne mora biti gust. Apstraktni Košijev problem je proučavan za težinske Banahove prostore kao i za odgovarujuće prostora ultradistribucija. Takođe su date i primene za određene klase jednačina.
Faculty:
University of Novi Sad, Faculty of Science
Date:
18-10-2014
Keywords:
Convolutors / Konvolutori / Multiplikatori / Ultradistribucione polugrupe / Hiperfunkcione polugrupe / Košijev problem / Multipliers / Ultradistribution semigroups / Hyperfunction semigroups / Cauchy problem
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URI
http://nardus.mpn.gov.rs/handle/123456789/1647
http://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija140265995221725.pdf?controlNumber=(BISIS)87864&fileName=140265995221725.pdf&id=2233&source=NaRDuS&language=sr
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http://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisije140265995793063.pdf?controlNumber=(BISIS)87864&fileName=140265995793063.pdf&id=2234&source=NaRDuS&language=sr

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