Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1142
The validity of the present theorem in the range 1 < p S2 now follows at once from its validity in the range 2 < p Soo and from Lemma 9.14 . Q.E.D. In what follows , we will use the symbols p and n to denote the n continuous extension ...
The validity of the present theorem in the range 1 < p S2 now follows at once from its validity in the range 2 < p Soo and from Lemma 9.14 . Q.E.D. In what follows , we will use the symbols p and n to denote the n continuous extension ...
Page 1684
Hence , it is quite sufficient to prove the present lemma for the special case m = 0. By Corollary 2 again , each derivative g of order 1 of F belongs to Lp ' ( E7 ) ( and has compact carrier ) , for every p satisfying the inequality ...
Hence , it is quite sufficient to prove the present lemma for the special case m = 0. By Corollary 2 again , each derivative g of order 1 of F belongs to Lp ' ( E7 ) ( and has compact carrier ) , for every p satisfying the inequality ...
Page 1692
( r ) –1m , ( a ) o dx = 0 . m , m , 00 proving the present lemma . Q.E.D. 9 COROLLARY . The conclusions of Corollary 6 and Lemma 8 remain valid even if the open set I of these results is replaced by the cube C - { re E " ; < , i = 1 ...
( r ) –1m , ( a ) o dx = 0 . m , m , 00 proving the present lemma . Q.E.D. 9 COROLLARY . The conclusions of Corollary 6 and Lemma 8 remain valid even if the open set I of these results is replaced by the cube C - { re E " ; < , i = 1 ...
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