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Choi, Man-Duen; Lam, Tsit-Yuen; Reznick, Bruce

Real zeros for positive semidefinite forms. I. (English) Zbl 0415.10018

Math. Z. 171, 1-26 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0415.10018

Cited in 4 Reviews
Cited in 36 Documents

MSC:

11E76 Forms of degree higher than two
14Pxx Real algebraic and real-analytic geometry
14N05 Projective techniques in algebraic geometry

Keywords:

real zeros; positive semidefinite forms; higher degree forms; sums of squares; Hilbert 16th problem
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Full Text: DOI EuDML

References:

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[2] Apostol, T.: Calculus, (2nd Edition), Vol. II. New York: John Wiley 1969 · Zbl 0185.11402
[3] Choi, M.D.: Positive semidefinite biquadratic forms. Linear Algebra and Appl.12, 95-100 (1975) · Zbl 0336.15014 · doi:10.1016/0024-3795(75)90058-0
[4] Choi, M.D., Lam, T.Y.: Extremal positive semidefinite forms. Math. Ann.231, 1-18 (1977) · doi:10.1007/BF01360024
[5] Choi, M.D., Lam, T.U.: An old question of Hilbert. In: Proceedings of the Quadratic Form Conference 1976 (ed. G. Orzech), pp. 385-405. Queen’s Papers in Pure and Applied Mathematics Vol.46, Kingston, Ontario: Queen’s University
[6] Choi, M.D., Lam, T.Y., Reznick, B.: Classification of symmetric positive semidefinite quartics. In preparation
[7] Choi, M.D., Lam, T.Y., Reznick, B.: In preparation
[8] Choi, M.D., Lam, T.Y., Reznick, B., Rosenberg, A.: Sums of squares in some integral domains. J. Algebra (to appear) · Zbl 0433.10010
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[10] Djokovi?, D.?.: Hermitian matrices over polynomial rings. J. Algebra43, 359-374 (1976) · Zbl 0343.15006 · doi:10.1016/0021-8693(76)90119-8
[11] Fulton, W.: Algebraic Curves. Reading, Mass.: Benjamin 1969 · Zbl 0181.23901
[12] Gudkov, D.A., Utkin, G.A.: Nine Papers on Hilbert’s 16th Problem. A.M.S. Translations, Series 2, Vol.112, Providence, R.I.: American Mathematical Society
[13] Hilbert, D.: Über die Darstellung definiter Formen als Summe von Formquadraten. Math. Ann.32, 342-350 (1888) · JFM 20.0198.02 · doi:10.1007/BF01443605
[14] Hilbert, D.: Über die reellen Züge algebraischer Kurven. Math. Ann.38, 115-138 (1891) · JFM 23.0753.02 · doi:10.1007/BF01212696
[15] Hilbert, D.: Mathematische Probleme. Göttinger Nachrichten 1900, 253-297. (See also: Mathematical Developments Arising From Hilbert Problems (ed. F. Browder), Proc. Symp. in Pure Math. Vol.28. Providence: Amer. Math. Soc. · JFM 31.0068.03
[16] Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. Cambridge-London: Cambridge University Press 1964
[17] Jakubovi?, V.A.: Factorization of symmetric matrix polynomials. Dokl. Akad. Nauk SSSR194, 532-535 (1970)
[18] Popov, V.M.: Hyperstability of Control Systems. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0276.93033
[19] Reznick, B.: Extremal psd forms with few terms. Duke Math. J.45, 363-374 (1978) · Zbl 0395.10037 · doi:10.1215/S0012-7094-78-04519-2
[20] Robinson, R.M.: Some definite polynomials which are not sums of squares of real polynomials. In: Selected Questions of Algebra and Logic, pp. 264-282, Acad. Sci. USSR 1973
[21] Rosenblum, M., Rovnyak, J.: The factorization problem for nonnegative operator valued functions. Bull. Amer. Math. Soc.77, 287-318 (1971) · Zbl 0214.12102 · doi:10.1090/S0002-9904-1971-12671-X
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