ON CLASSIFICATION AND SUPERPOSITION PRINCIPLES FOR NONLINEAR OPERATORS.
Abstract
Superpositions (ways of expressing a solution of an equation as a function of other solutions of the equation) for nonlinear operators are discussed. For operators having certain kinds of superpositions, a unique representation involving their superposition and additively linear operators is given. Equivalence classes of operators are obtained, each class being composed of operators having a given superposition. Generalized translations of operators are defined in terms of the superpositions. The classification of operators is further extended, and a number of well-known nonlinear differential operators are shown to belong to certain of these extended classes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1965
- Accession Number
- AD0624268
Entities
People
- Alfred Inselberg
Organizations
- University of Illinois Urbana–Champaign