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On positive definite differences of multilinear forms and their representation

Published online by Cambridge University Press:  14 November 2011

Alexander Kovačec
Alexander Kovačec
Affiliation:
Mathematisches Institut der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
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Synopsis

We study the evaluation of multilinear forms under arbitrary rearrangements of the entries of increasing n-tuples x(1), x(2),…, x(m), and we show that the difference of two such multilinear forms under certain circumstances can be written as a sum of obviously definite forms.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 97 - 108
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Beckenbach, E. F. (ed.) General inequalities III (Proc. of a conference held at Oberwolfach 1981) (Basel: Birkhauser, 1983).CrossRefGoogle Scholar
2Fan, Ky. Subadditive functions on a distributive lattice and an extension of Szasz's inequality. J. Math. Anal. Appl. 18 (1967), 262–268.CrossRefGoogle Scholar
3Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities (Cambridge, 1934 and 1952).Google Scholar
4Hollander, M. F., Proschan, F. and Sethuraman, J.. Functions decreasing in transposition and their applications in ranking problems. Ann. Statist. 5 (1977), 722–733.CrossRefGoogle Scholar
5Kovačec, A.. An algorithmic approach to inequalities. Appears in [1].Google Scholar
6Kovačec, A.. Uber den algorithmischen Nachweis von Ungleichungen I. Monatsh. Math. 92 (1981), 19–35.CrossRefGoogle Scholar
7Lehmann, E. L.. Some concepts of dependence. Ann. Math. Statist. 37 (1966), 1137–1155.CrossRefGoogle Scholar
8Marshall, A. W. and Olkin, I. O.. Inequalities: Theory of Majorization and its Applications (NewYork: Academic Press, 1979).Google Scholar
9Mine, H.. Rearrangement inequalities. Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), 339–345.Google Scholar
10Mitronovic, D. S.. Analytic Inequalities (Berlin: Springer, 1970).CrossRefGoogle Scholar
11Pecaric, J. E.. A generalization of an inequality of Ky Fan. Publ. Elektrotechn. Fak. Univ. Beograd Ser. Mat. Fiz. N694.Google Scholar
12Popoviciu, T.. On an inequality (Romanian). Gaz. Mat. Fiz. 64 (1959), 451–461.Google Scholar
13Ruderman, H. D.. Two new inequalities. Amer. Math. Monthly 59 (1952), 29–32.Google Scholar
14Sobel, M.. On a generalization of an inequality of Hardy, Littlewood and Polya. Proc. Amer. Math. Soc. 5 (1954), 592–602.Google Scholar