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

Abstract

<p>We are study the spaces of convolutors and multipliers in the spaces of<br />tempered ultradistributions. There given theorems which gives us the characteri-zation of all the elements which belongs to spaces of convolutors and multipliers.<br />Structural theorem for ultradistribution semigroups and exponential ultradistri-bution semigroups is given. Fourier hyperfunction semigroups and hyperfunction<br />semigroups with non-densely dened generators are analyzed and also structural<br />theorems and spectral characterizations give necessary and sucient conditions<br />for the existence of such semigroups generated by a closed not necessarily densely<br />dened operator A. The abstract Cauchy problem is considered in the Banach<br />valued weighted Beurling ultradistribution setting and given some applications on<br />particular equations.</p>

<p>U disertaciji se proučavaju prostor konvolutora i multiplikatora na prostorima temperiranih ultradistribucija. Dokazane su&nbsp;teoreme koji karakteri&scaron;u elemente prostora konvolutora i multiplikatora. Date su strukturne teoreme za ultradistribucione &nbsp;polugrupe&nbsp;i eksponenecijalne polugrupe. Furijeve huperfunkciske polugrupe i&nbsp;hiperfunkciske polugrupe sa generatorima koji su negusto definisani&nbsp;<br />su analizirani, takođe su date strukturne teoreme i spektralne karakterizacije kao i dovoljni uslovi za postojenje na takvih polugrupa&nbsp;za operator A koji ne mora biti gust. Apstraktni Ko&scaron;ijev problem je&nbsp;proučavan za težinske Banahove prostore kao i za odgovarujuće prostora ultradistribucija. Takođe su date i primene za određene klase<br />jednačina.</p>