ALGEBRAIC CHARACTERIZATION OF POLYNOMIALS WHOSE ZEROS LIE IN CERTAIN ALGEBRAIC DOMAINS | Zendy

R. E. Kalman | Zendy

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ALGEBRAIC CHARACTERIZATION OF POLYNOMIALS WHOSE ZEROS LIE IN CERTAIN ALGEBRAIC DOMAINS

Author(s) -

R. E. Kalman

Publication year - 1969

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.64.3.818

Subject(s) - algebraic number , mathematics , algebra over a field , characterization (materials science) , function field of an algebraic variety , algebraic function , real algebraic geometry , pure mathematics , dimension of an algebraic variety , algebraic cycle , physics , mathematical analysis , optics

A new algebraic criterion is given for a polynomial φ with complex coefficients to have all its zeros in a certain type of algebraic region T of the complex plane. In particular, T may be any circle or half plane. The criterion is effectively computable from the coefficients of the polynomial φ. The classical results of Hermite, Hurwitz, Lyapunov, Schur-Cohn, and others appear as special cases of the new criterion.

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