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has been cited by the following article:

• TITLE: A Note on the Structure of Affine Subspaces of L2(Rd)

  AUTHORS: Fengying Zhou, Xiaoyong Xu

  KEYWORDS: Affine Subspace, Reducing Subspace, Shift Invariant Subspace, Orthogonal Sum

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.2, January 28, 2015

  ABSTRACT: This paper investigates the structure of general affine subspaces of L2(Rd) . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a purely non-reducing subspace, and every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces when |detA| = 2.