1. Classical facts concerning the Cauchy problem for hyperbolic and parabolic second order equations can be found in the monographs of Hörmander [1963], Courant [1962], and in the survey paper of Il’in, Kalashnikov, and Olejnik [1962]; these also contain a host of historic material (see also Courant, Friedrichs and Lewy [1928] and Leray [1953]).
2. Petrovskij’s results on the Cauchy problem are presented in the original papers (Petrovskij [1938, 1937]) (see also Schwarz [1950]). Further results on the Cauchy problem for equations with constant coefficients can be found in the monographs of Gel’fand and Shilov [1958], Palamodov [1967], Hörmander [1963], and Hörmander [1983]. On the Cauchy problem for higher order hyperbolic equations and systems see Petrovski [1937], Levi [1907], Gårding [1957], Courant [1962], Hörmander [1963, 1983]. The basic material concerning the Cauchy problem for parabolic equations is contained in the monograph of Ejdel’man [1964].
3. Theory of distributions is presented in the monographs of Schwarz [1950/51], Leray [1953], Vladimirov [1978], Gel’fand and Shilov [1958], Palamodov [1967], Hörmander [1963, 1983]. Functional spaces and their embedding theorems can be found in the books of Sobolev [1950], Palamodov [1967], Hörmander [1963, 1983], and Taylor [1981].
4. Proofs of the main results of Chapter 1 can be found in Volevich and Gindikin [1972]; further references are in Volevich and Gindikin [1982].
5. For energy methods see Volevich [1974], Volevich and Gindikin [1968, 1980], Gindikin [1974].