Invariant subspaces generated by a single function in the Polydisk

Koca B. B., Sadik N.

MATHEMATICAL NOTES, cilt.102, ss.193-197, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 102
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1134/s0001434617070215
  • Dergi Adı: MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.193-197
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this study, we partially answer a question left open in Rudin's book "Function Theory in Polydisks" on the structure of invariant subspaces of the Hardy space H (2)(U (n) ) on the polydisk U (n) . We completely describe all invariant subspaces generated by a single function in the polydisk. Then, using our results, we prove the unitary equivalence of this type of invariant subspace and a characterization of outer functions in H (2)(U (n) ).