## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1142

The validity of the

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

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

( 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 ...### What people are saying - Write a review

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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero