Properties on the unit circle of polynomials with unimodular coefficients
Donald J. Newman and André Giroux
Proc. Amer. Math. Soc. 109 (1990), 113-116
Primary 30C15; Secondary 30C10, 42A16, 42A28
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Abstract: A concrete explicit construction of a unimodular polynomial with prescribed zeros on the unit circle is given. More precisely a polynomial is produced for which for all and for which for a given set of , and elsewhere on . It is further shown how to extend this construction so as to maintain these properties and force the maximum of to occur at any given number and . The dependence of on is exponential, but there is rėason to believe that this is actually necessary and not just a weakness of the method.
J. S. Byrnes and D. J. Newman, Null steering employing polynomials with restricted coefficients, IEEE Transactions on Antennas and Propagation 36 (1988), 301-303.
- J. S. Byrnes and D. J. Newman, Null steering employing polynomials with restricted coefficients, IEEE Transactions on Antennas and Propagation 36 (1988), 301-303.
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