On an Eigenvalue Problem for Some Nonlinear Transformations of Multi-dimensional Arrays.

Authors :: Gohberg, I.
Alpay, D.
Arazy, J.
Atzmon, A.
Ball, J. A.
Ben-Artzi, A.
Bercovici, H.
Böttcher, A.
Clancey, K.
Coburn, L. A.
Curto, R. E.
Davidson, K. R.
Douglas, R. G.
Dijksma, A.
Dym, H.
Fuhrmann, P. A.
Gramsch, B.
Helton, J. A.
Kaashoek, M. A.
Kaper, H. G.
Source :: Recent Advances in Matrix & Operator Theory; 2008, p197-210, 14p
Publication Year :: 2008
Abstract: It is shown that certain transformations of multi-dimensional arrays posses unique positive solutions. These transformations are composed of linear components defined in terms of Stieltjes matrices, and semi-linear components similar to u → ku3. In particular, the analysis of the linear components extends some results of the Perron-Frobenius theory to multi-dimensional arrays. [ABSTRACT FROM AUTHOR]

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