Twisted duality of the CAR-Algebra

We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use modular theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof. As a byproduct of the proof we obtain an explicit and simple formula for the graph of the modular operator. This formula can be also applied to fermionic free nets, hence giving a formula of the modular operator for any double cone.Comment: 32 pages, Latex2e, to appear in Journal of Mathematical Physic

Loop group factorization of biorthogonal wavelet bases

We present a factorization theorem for certain polynomial loops in the matrix group GL(2, C). The theorem leads to the construction of an algorithm for the factorization of pairs of biorthogonal filters with finite impulse response in simple terms, resulting in a reduction of the complexity of the corresponding wavelet transform. (orig.)Available from TIB Hannover: RR 1596(281) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman