Invariant subspaces generated by a single function in the Polydisk


Koca B. B., Sadik N.

MATHEMATICAL NOTES, vol.102, pp.193-197, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102
  • Publication Date: 2017
  • Doi Number: 10.1134/s0001434617070215
  • Journal Name: MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.193-197
  • Istanbul University Affiliated: Yes

Abstract

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) ).