The purpose of this chapter is to give a condensed exposition of those definitions and results of distribution theory which will be required in the following chapters. The reader may thus consult Schwartz  for a more detailed study of almost all topics discussed here. An exception is Definition 1.3.3 and the related Theorem 1.7.8, which are based on an idea of Ehrenpreis  (see also Malgrange  and Hörmander ). In section 1.8 we have added a definition of distributions on manifolds which will be needed in Chapter X. We have also inserted there a brief sketch of the classical integration theory for the characteristic equation.
KeywordsDifferential Operator Open Subset Compact Subset Linear Form Compact Support
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