Embedding singular linear system with initial condition into distribution space

Abstract: For inconsistent initial value problem of singular linear system, passing from classical solution to distributional solution is formulated as a process of embedding the system with initial condition into distribution space. Three technical notions, function space on with given initial value, consistent extension of the pair of the function space and input, and order exchange of the two operations of embedding and differentiating, result in a rigorous definition of distributional solution. [Copyright &y& Elsevier]