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Inverse problems for unilevel block α-circulants

Authors


  • Dedicated to Professor Biswa Nath Datta.

Correspondence to: W. Trench, 659 Hopkinton Road, Hopkinton, NH 03229 USA.

E-mail: wtrench@trinity.edu

SUMMARY

We consider the following inverse problems for the class inline image of unilevel block α-circulants inline image, where k > 1, C0, C1, …, inline image, α ∈ {1,2, … ,k −1}, gcd(α,k) = 1, and ∥ ⋅ ∥ is the Frobenius norm.

Problem 1 Find necessary and sufficient conditions on inline image and inline image for the existence of inline image such that CZ = W, and find all such C if the conditions are satisfied.

Problem 2 For arbitrary inline image and inline image, find

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characterize the class

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and find C in this class with minimum norm.

Problem 3 If inline image is given, find

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and find inline image such that ∥ CA ∥ = σα(Z,W,A).

We also consider slightly modified problems for the case where gcd(α,k) > 1. Copyright © 2011 John Wiley & Sons, Ltd.

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