The abstract Cauchy problem. (English) Zbl 0326.35007


35F05 Linear first-order PDEs
47D03 Groups and semigroups of linear operators
47F05 General theory of partial differential operators
47A50 Equations and inequalities involving linear operators, with vector unknowns
Full Text: DOI


[1] Carroll, R.: On some hyperbolic equations with operator coefficients. Proc. Japan acad. 49, 233-238 (1973) · Zbl 0273.35049
[2] Donaldson, J. A.: The Cauchy problem for a first order system of abstract operator equations. Bull. amer. Math. soc. 81, 576-578 (1975) · Zbl 0307.35021
[3] J. A. Donaldson, A uniqueness class for two improperly posed problems in mathematical physics, in ”Improperly Posed Boundary Value Problems” (A. Carasso and A. P. Stone, Eds.), Research Notes in Mathematics Series, No. 1, Pitman, Belmont, California. · Zbl 0319.35065
[4] Donaldson, J. A.: The abstract Cauchy problem and Banach space valued distributions. Mathematical report #13 (1975)
[5] Gel’fand, I. M.; Silov, G. E.: Fourier transforms of rapidly increasing functions and questions of the uniqueness of the solution of Cauchy’s problem. Uspehi mat. Nauk 8, 3-54 (1953)
[6] Gel’fand, I. M.; Silov, G. E.: Generalized functions. 1 (1964)
[7] Gel’fand, I. M.; Silov, G. E.: Generalized functions. 3 (1967)
[8] Hersh, R.: Direct solutions of general one-dimensional linear parabolic equation via an abstract Plancherel formula. Proc. nat. Acad. sci. USA 63, 648-654 (1969) · Zbl 0179.43001
[9] Hersh, R.: Explicit solution of a class of higher-order abstract Cauchy problems. J. differential equations 8, 570-579 (1970) · Zbl 0208.38603
[10] Hille, E.: Une généralisation du problème de Cauchy. Ann. inst. Fourier (Grenoble) 4, 31-40 (1952) · Zbl 0055.34503
[11] Hille, E.: Functional analysis and semi-groups. AMS colloquium publications 31 (1948) · Zbl 0033.06501
[12] J. Sandefur, Abstract Cauchy Problems, to appear. · Zbl 0358.35068
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.