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Interpolation classes and matrix means 

Authors: 

Dinh Trung Hoa, Osaka H. and Ho Minh Toan 

Source title: 
Banach Journal of Mathematical Analysis, 9(3): 140-152 , 2015 (ISI)
Academic year of acceptance: 
2015-2016
Abstract: 

Using a `local' integral representation of a matrix connection of order n corresponding to an interpolation function of the same order, for each integer n, we can describe an injective map from the class of matrix connections of order n to the class of positive n-monotone functions on (0,∞)(0,∞) and the range of this corresponding covers the class of interpolation functions of order 2n. In particular, the space of symmetric connections is isomorphic to the space of symmetric positive n-monotone functions. Moreover, we show that, for each n, the class of n-connections extremely contains that of (n+2)-connections.