توصيفگر ها :
اﺑﺮﮔﺮوه , ﺟﺒﺮ ﻓﻮرﯾﻪ , ﺟﺒﺮﻫﺎي ﺿﺮﺑﮕﺮي , وﯾﮋﮔﯽ ﻫﻤﻮﻟﻮژﯾﮏ
چكيده فارسي :
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
چكيده انگليسي :
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.
