By Andrzej Boguslawski

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15) K2 ID9 * z*W (t) l < - r(l~ll) e PIITI dT I -< -F(I~ll) -~ (Mr (i)) IVl ft ~ (MF(1)) I~l jltl ~ I (t-T) h-I e u21t-TITI~II-I o h+]~ll-1 Itl B(h,I~ll). 89 With lemma i the result easily follows. 2. REDUCTION OF THE DIFFERENTIAL EQUATION TO AN INTEGRAL EQUATION From hypothesis H. 17) b - t 6 S~ and ] 1 SVfo (0) , ~ ( t ) = m--~ 1 ~v q) ( o , t ) i f ~ 6 I, t 6 Sj . From Cauchy's formula for derivatives of analytic functions and hypothesis H. 18) 1 -i ~lltl It~ 1 e , where Ko is the maximum of K (cf.

15) ~" C~ as XA --) 00 In particular, if w . is bounded from zero and bounded above, it is sufficient that q, w' and w" be bounded on a sequence of intervals of unbounded lengths. 15) together with the previous arguments. 12), involving higher derivatives, have often been used to get, stability theorems (13) . However it is not clear how to extend them to the matrix case (1,3), or how to form them in general. 23 REFERENCES I. F. V. Royal Soc. (A), 2. 73(1975), 167-198. I. Brinck, Self-adjointness and spectra of Sturm-Liouville operators, Math.

18) - --2 - 82 + e _< p a r g x _< ~ - 81 - e(e where 81 = 82 = - a r g ~ in case 2. 5) 33 This may be s h o w n using a rank reduction scheme of T U R R I T T I N [21]: substitute ~T x = ~i/p, u(~) = (~o(~) ' "''' (~))T Yp-I v(~) = (~o(~)..... ~p-i (~))T. 4) M(~) to + v(~), ~ Z M ~-m, 0 m we may deduce of Mo w i t h nlp. 1) Hence Mo theorem we have to t h e c a s e AIo © 1 I 1 p that M ° has nlP multiplicity nonsingular. 19) a regular "'- A op-I ..... A I o "- of z e r o s is s i m i l a r I to A1 o • to d i a g both 0 is e i g e n v a l u e { 0 , M 22}O w h e r e and the result singular p = I by dividing and that "A o o point sides M 22o is follows.

### A Note on Two Dogmas in Pragmatics by Andrzej Boguslawski

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