Vol. 37, No. 2, 1971

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Algebraic structure for a set of nonlinear integral operations

David Lowell Lovelady

Vol. 37 (1971), No. 2, 421–427

A generalized addition is introduced for a set of generators, and a generalized multiplication is introduced for a set of evolution systems. Then the mapping which takes a generator to the corresponding evolution system becomes an isomorphism. Necessary and sufficient conditions are found for the generalized addition to reduce to addition, and hence, under these conditions, we are able to write a formula for the evolution system generated by the sum of two generators.

Mathematical Subject Classification 2000
Primary: 47D05
Secondary: 47H99
Received: 4 June 1970
Published: 1 May 1971
David Lowell Lovelady