Cauchy's Problem for Hyperbolic Equations: Lectures, Winter and Spring Quarteres, 1957, University of Chicago, Parts 1-2University of Chicago, 1957 - Differential equations, Partial |
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Cauchy's Problem for Hyperbolic Equations: Winter and Spring Quarters, 1957 ... Lars Garding,G. Bergendahl No preview available - 2013 |
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analogous assumptions Banach space bounded coefficients bounded variation Cauchy's problem characteristic polynomial continuous functions converges D₁ D₂ h defined denoted derivatives of order double differential operator double order dual dual space duality equivalence f ɛ fact finishes the proof finite following lemma formula function f Hahn-Banach theorem Helly's theorem Hence hermitian Hölder's inequality homogeneous hyperbolic equations hyperbolic operators implies infinitely differentiable integrable functions left side lemma Leray linear functional linear homeomorphism Lip¹ Lipp locally integrable locally integrable function norm normal notation operator of order order m;m order m+1 partial adjoints problem for hyperbolic remains to prove Remark replaced right side satisfying sense suffices to prove tends to zero term theorem 7.1 totally positive unique solution vanishing in neighborhoods weakly dense write