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The Invariance of the Core Subspace

  • Kathy D. Merrill
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

The invariance of the core subspace V0 of a GMRA under the group Γ of unitary operators implies the existence of a unitary representation of Γ on V0, thus enabling the use of tools from abstract harmonic analysis. Because of the required condition δ−1Γδ ⊂ Γ, the invariance of V0 also gives invariance of Vj for j > 0, and thus representations of Γ there as well. The invariance of V1 in turn implies the invariance of W0 = V1 ∖ V0, where the representation of Γ is useful in proving the existence of orthonormal or Parseval wavelets. In this chapter we explore results that follow from analyzing these representations of Γ.

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Authors and Affiliations

  • Kathy D. Merrill
    • 1
  1. 1.Department of MathematicsThe Colorado CollegeColorado SpringsUSA

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