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The Central Ando Dilation and Related Orthogonality Properties

✍ Scribed by W.S. Li; D. Timotin


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
249 KB
Volume
154
Category
Article
ISSN
0022-1236

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✦ Synopsis


A pair of commuting contractions on a Hilbert space has in general many nonisomorphic minimal unitary dilations. We show that there is a ``distinguished'' one. This can be viewed in many respects as an analogue of the central intertwining lifting in the family of all intertwining liftings of a contraction.


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Suppose that m(ΞΎ ) is a trigonometric polynomial with period 1 satisfying m(0) = 1 and |m(ΞΎ , is related to the zeros of m(ΞΎ ). In 1995, A. Cohen and R. D. Ryan, "Wavelets and Multiscale Signal Processing," Chapman & Hall, proved that if m(ΞΎ ) has no zeros in [-1 6 , 1 6 ], then Ο•(x) is an orthogon