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 → ku 3. In particular, the analysis of the linear components extends some results of the Perron-Frobenius theory to multi-dimensional arrays.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Kaur, S.P., Koltracht, I. (2007). On an Eigenvalue Problem for Some Nonlinear Transformations of Multi-dimensional Arrays. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_12
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DOI: https://doi.org/10.1007/978-3-7643-8539-2_12
Publisher Name: Birkhäuser Basel
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