Tez özetleri Astronomi ve Uzay Bilimleri Anabilim Dalı

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Abstract Harmonıc Analysıs of Weıghted Orlıcz Spaces
This thesis is about the abstract harmonic analysis of weighted Orlicz spaces and consists of three part; Introduction, General Sections and Results. The first two parts are related to preliminary process and the third part is the main part of the thesis.
In the first part, it is explained the aim and content of the thesis. In the second part, we recall main definitions and theorems which are used through the thesis.
The third part is the main part and it splits into two sections.
In the first section, firstly we give the different definitions of the functions Φ which are used to define the Orlicz space in the literature and investigate the relationships between these functions. Secondly, given a locally compact Abelian group G, a weight function w and a Young function Φ, then the weighted Orlicz space, denoted by L^Φ_w(G), is introduced and it is shown that L^Φ_w(G) is a Banach space and it is investigated the inclusions with respect to weight function w and Young function Φ. Also, we studied abstract harmonic analysis properties of the space L^Φ_w(G) such as, density of continuous compactly supported functions space, translation invariance and continuity of the translations.
The second section is the main goal of this thesis and in this section it is studied to find a necessary and sufficient conditions for the Banach algebra structure of the weighted Orlicz space and it is investigated properties of these Banach algebras. On the other hand, these Banach algebras are called weighted Orlicz algebras. Especially, the Banach algebra structure with respect to convolution is important. Because, in this thesis it is concentrated on the properties such as, existence of the identity and bounded approximate identity, characterization of the maximal ideals space, semisimplicity and determining the closed ideals of the weighted Orlicz algebra which comes from the Banach algebra structure of the algebra L^Φ_w(G). In connection with this, we investigate the relationship between the Banach algebra and the locally compact topolojical group.