Norm and almost everywhere convergence of convolution powers
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
Let G be a locally compact abelian group with the dual group ?, M (G), the measure algebra of G, and Mr (G), the largest regular subalgebra of M (G). For a power bounded measure µ ? M (G), we put Fµ = {? ? ? : µb (?) = 1} and Eµ = {? ? ? : |µb (?)| = 1} , where µb is the Fourier-Stieltjes transform of µ. Let (?, ?, m) be a ??finite positive measure space and let ? = {?g}g?G be an action of G in (?, ?, m) by invertible measure preserving transformations. Any action ? induces a representation T = {Tg}g?G of G on L p (?) (1 ? p < ?) by invertible isometries, where (Tgf) (?) = f (?g?). If ? is continuous, then for any µ ? M (G), we can define a bounded linear operator on L p (?) (1 ? p < ?) associated with µ, denoted by Tµ, which integrates Tg with respect to µ. Theorem. Let µ ? Mr (G) be power bounded and 1 < p < ?. If Fµ = Eµ, then the sequence { Tn µ f } converges strongly for every f ? L p (G).
Açıklama
Anahtar Kelimeler
Abelian group, Measure algebra, L p -space, Convergence
Kaynak
International Conference of Mathematical Sciences (ICMS 2019)
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Mustafayev, H. (2019).Norm and almost everywhere convergence of convolution powers. International Conference of Mathematical Sciences (ICMS 2019). s. 42.
