ERGODIC PROPERTIES OF CONVOLUTION OPERATORS IN GROUP ALGEBRAS


Mustafayev H., Topal H.

COLLOQUIUM MATHEMATICUM, cilt.165, sa.2, ss.321-340, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 165 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.4064/cm8214-6-2020
  • Dergi Adı: COLLOQUIUM MATHEMATICUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.321-340
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Let G be a locally compact abelian group and let L-1 (G) and M(G) be respectively the group algebra and the convolution measure algebra of G. For mu is an element of M(G), let T(mu)f = mu * f be the convolution operator on L-1(G). A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0)parallel to mu(n)parallel to(1) < infinity, where mu(n) denotes the nth convolution power of mu. We study some ergodic properties of the convolution operator T-mu, in the case when mu is power bounded. We also present some results concerning almost everywhere convergence of the sequence {T(mu)(n)f} in L-1 (G).