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**Extra resources for A Cauchy Problem for an Ultrahyperbolic Equation**

**Sample text**

Bylov and N. A. Izobov, "Necessary and sufficient conditions for the stability of characteristic exponents of a linear system," Differents. , ~, No. ]0, 1794-1803 (1959). R. E. Vinograd, "On the central characteristic exponent of a system of differential equations " Mat Sb. 42, 207-222 (1957). Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach. Space [in Russian], Nauka, Moscow (1970). B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (]967).

Then by C o r o l l a r y 8 . 6 , a p p l i e d t o s u b s p a c e L, t h e r e s u c h t h a t ~L ~ S ( B ) . But f r o m i n e q u a l i t i e s ( 7 . 8 ) and ( 1 1 . 6) COROLLARY 1 1 . 5 . and sup ~,k(B) >/~]L. The m a x i m a l i - t h ( 1 1. 1O) B6 ~3(A) ( 1 1 . 5, ~k(B)/> ~L. 6). , for every equation A ~ %m~x (A) = COROLLARY 1 1 . 6 . For every equation A~ a unique space of the i-th exponent, namely, sup %~ (B). B6~(A) and e v e r y number i ~ {1, . . 9~ exists Proof. L e t L b e some s p a c e o f t h e i - t h e x p o n e n t o f e q u a t i o n A ( t h e e x i s t e n c e o f L i s p r o v e d i n Lemma 1 1 .

0 Also, we denote by Wz(~) the set of those bases S which satisfy the following conditions at least one t El [T, O]: S~- w (r Then, as a consequence of the nondiagonalizability to) one can find a t s ~ R + such that Moreover, there is a number T(a, for t). B. Now suppose that equation A is such that lira T(c,, to)