doctoral thesis
Michael Kaplin (Author), Marjeta Kramar Fijavž (Mentor), Marko Kandić (Co-mentor)

Abstract

V disertaciji uvedemo in obravnavamo pojme relativno enakomerne zveznosti in krepke zveznosti glede na relativno enakomerno topologijo za polgrupe operatorjev na splošnih vektorskih mrežah. Z njihovo pomočjo obravnavamo polgrupe na prostorih, ki niso lokalno konveksni, kot so ▫$L^p({\mathbb R})$▫ za ▫$0 < p < 1$▫, in nekompletnih prostorih ▫${\rm Lip}({\mathbb R})$▫, ▫${\rm UC}({\mathbb R})$▫ in ▫${\rm C}_c({\mathbb R})$▫. Predstavimo tudi primere relativno enakomerno zveznih polgrup kot so Koopmanove polgrupe in Ornstein-Uhlenbeckova polgrupa. Predstavimo pojme relativno enakomerno zveznih, odvedljivih in integrabilnih funkcij na ▫${\mathbb R}_+$▫. Z njihovo pomočjo obravnavamo generatorje relativno enakomerno zveznih polgrup. Glavni rezultat je izrek tipa Hille-Yosida, ki nudi potrebne in zadostne pogoje, da je operator generator eksponentno urejenostno omejene, relativno enakomerno zvezne in pozitivne polgrupe.

Keywords

vector lattices;relatively uniform convergence;relatively uniform topology;relatively uniform continuity;positive operator semigroups;strongly continuous semigroups;Hille-Yosida theorem;

Data

Language: English
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UL FGG - Faculty of Civil and Geodetic Engineering
Publisher: [M. Kaplin]
UDC: 517.982(043.3)
COBISS: 32235523 Link will open in a new window
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Other data

Secondary language: Slovenian
Secondary title: Relativno enakomerno zvezne polgrupe pozitivnih operatorjev na vektorskih mrežah
Secondary abstract: In this thesis we introduce and study notions of relatively uniform continuity and strong continuity with respect to the relatively uniform topology for semigroups of operators on general vector lattices. These notions allow us to study semigroups on non-locally convex spaces, such as ▫$L^p({\mathbb R})$▫ for ▫$0 < p < 1$▫, and non-complete spaces, such as ▫${\rm Lip}({\mathbb R})$▫, ▫${\rm UC}({\mathbb R})$▫, and ▫${\rm C}_c({\mathbb R})$▫. We provide examples of relatively uniformly continuous semigroups such as Koopman semigroups and the Ornstein-Uhlenbeck semigroup. We introduce notions of relatively uniformly continuous, differentiable, and integrable functions on ▫${\mathbb R}_+$▫ which enable us to study generators of relatively uniformly continuous semigroups. Our main result is a Hille-Yosida type theorem which provides sufficient and necessary conditions for an operator to be the generator of an exponentially order bounded, relatively uniformly continuous, positive semigroup.
Secondary keywords: vektorske mreže;relativno enakomerna konvergenca;relativno enakomerna topologija;relativno enakomerna zveznost;pozitivne operatorske polgrupe;krepko zvezne polgrupe;izrek Hille-Yosida;
Type (COBISS): Doctoral dissertation
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. Ljubljana, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 3. stopnja
Pages: XII, 91 str.
ID: 12046411