9594

8849

كارشناسي ارشد

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

هشت،96ص.: نمودار

ص.ع.به فارسي و انگليسي

رياضي

ID8849

Positivity and conditional positivity of Loewner matrices Behrooz Heydarii b heydarii@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Seyed Mahmoud Manjegani manjgani@cc iut ac ir Advisor Dr Mohammad Reza Koushesh koushesh@cc iut ac ir 2010 MSC 15A48 47A63 42A82 Keywords Loewner matrix Operator monotone Operator convex Positive semide nite Con ditionally positive de nite Conditionally negative de nite AbstractThis thesis is an extension and generalization of the work s done by Loewnerin 1934 9 10 give elementary proofs of the fact that the Loewner matri We f pi f pj corresponding to the function f t tr on 0 are positiveces pi pjsemide nite conditionally negative de nite and conditionally positive de nite for rin 0 1 1 2 and 2 3 respectively We show that in contrast to the interval 0 the Loewner matrices corresponding to an operator convex function on 1 1 neednot be conditionally negative de nite In addition to the matrices Lr the matrices pr pr i j too have been of interest It was shown by Kwong 13 that forKr pi pj0 r 1 these matrices are p s d Di erent proofs of this fact have been givenin 5 and 8 and in 4 it was shown that these matrices are not just p s d they arein nitely divisible in 9 we showed that for 1 r 3 the matrices Kr are c n d Thus in this respect the behaviour of the matrices Lr and Kr is di erent in the range1 r 3 The methods of this paper can be used to derive these results and mayprovide some further understanding

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