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For a complex polynomialand for a rational number  p , we consider the Schur stability problem of the  p th Hadamard power of  fWe show that there exist two numberssuch thatis Schur stable for everyand is not Schur stable for(or vice versa, depending on  f ). Also, we give simple sufficient conditions for the Schur stability of the Hadamard product of two complex polynomials. Numerical examples complete and illustrate the results.

Results on the Schur stability of the Hadamard powers and the Hadamard product of complex polynomials