19006

2126 دكتري

دكتري

آناليز هارمونيك

اصفهان : دانشگاه صنعتي اصفهان

1402

يك، 106ص

1402/08/17

كتابنامه

رياضي

رياضي

1402/08/17

2980161

باشد. در اين رساله به مطالعه جبر G يك ابرگروه فراكروي متناظر با گروه فشرده موضعي H فرض كنيم شرايط M(A(H)) و فضاهاي مرتبط با آن مي پردازيم. به عنوان مثال، با بررسي فضاي ضربگري A(H) فوريه را ارائه مي دهيم. همچنين نشان مي دهيم قضيه لپتين قابل توسيع به ابرگروه هاي H لازم و كافي براي گسستگي . در قسمتي M(A(H)) = B(H) ميانگين پذير است، اگر و تنها اگر G فراكروي است. به عبارت ديگر، گروه را مورد مطالعه قرار مي دهيم و به عنوان يك نتيجه نشان V N(H) و V N(H) ديگر از رساله، زيرفضاهاي است. سرانجام در فصل پاياني، برخي از ويژگي هاي V N(H) -زيرجبر C يك UCB(bH ) مي دهيم كه فضاي را بررسي مي كنيم. H و ساختارهاي توپولوژيك معادل با آن ها روي A(H) همولوژيك

Abstract harmonic analysis primarily focuses on investigating locally compact groups, examining their unitary representations, and exploring the function spaces connected to these groups. Among these function spaces, the Fourier and Fourier-Stieltjes algebras hold significant importance in the study of a locally compact group. Hypergroups represent generalized variations of locally compact groups. Recently, significant attention has been directed from harmonic analysts towards the inquiry of identifying which hypergroups possess enough inherent structure to render their Fourier space an algebra through pointwise multiplication. This query has been tackled by Amini and Medghalchi [3], as well as by Muruganandam [49,50]. In a noteworthy contribution, Muruganandam [50] has introduced a notable category of such hypergroups, namely ultraspherical hypergroups. These ultraspherical hypergroups encompass double coset hypergroups generated by compact subgroups within a locally compact group. Ultraspherical hypergroups emerge from locally compact groups and specific spherical projectors. However, in contrast to locally compact groups, they exhibit a wide range of behaviors and are considerably more challenging to approach than groups and the Fourier and Fourier-Stieltjes algebras associated with groups. In this thesis, our investigation delves into the properties of Banach algebras connected to Fourier algebras associated with ultraspherical hypergroups. Specifically, we establish several results concerning the classification of discrete and compact ultraspherical hypergroups in the context of multipliers of the Fourier algebra. Additionally, we explore Banach algebras in the dual space of the Fourier algebra.

مهدي نعمتي

علي رضا مدقالچي

محمود منجگاني , فاطمه ابطحي , محمد رضا قانعي