Impossibility of extending Polya's theorem to forms with arbitrary real exponents

[摘要] Polya proved that if a form (homogeneous polynomial) with real coefficients is positive on the nonnegative orthant (except at the origin), then it is the quotient of two real forms with no negative coefficients. While Polya's theorem extends, easily, from ordinary real forms to generalized real forms with arbitrary rational exponents, we show that it does not extend to generalized real forms with arbitrary real (possibly irrational) exponents. (C) 2008 Elsevier B.V. All rights reserved.

[发布日期] 2008-12-01

[效力级别]  Proceedings Paper