Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics

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Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 31
1998-03 発行

Extremum Problems on a Hilbert Network

Yamasaki, Maretsugu
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Description
As a generalization of a usual infinite network, a Hilbert network is defined as a pair of a graph and a resistance taking values in a Hilbert space. With the sets of nodes and arcs of the graph, we associate variables belonging to a Hilbert space. In this situation, we study several extremum problems related to Hilbert-valued functions on the set of nodes or arcs of the graph and their inverse relations.