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

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Page 1099

By elementary arguments such as those employed in the third paragraph of the proof of Lemma 6 , which we leave to the reader to elaborate in detail , we may conclude that to establish ( a ) in general it is

By elementary arguments such as those employed in the third paragraph of the proof of Lemma 6 , which we leave to the reader to elaborate in detail , we may conclude that to establish ( a ) in general it is

**sufficient**to consider the ...Page 1475

If we can show that o ( :, 22 ) has a zero in ( a , 2 , ) and a zero in [ z2 , b ) , we will have established that o ( :, 22 ) has at least n + 1 zeros in ( a , b ) , contradicting the fact that he is in Jn . It is

If we can show that o ( :, 22 ) has a zero in ( a , 2 , ) and a zero in [ z2 , b ) , we will have established that o ( :, 22 ) has at least n + 1 zeros in ( a , b ) , contradicting the fact that he is in Jn . It is

**sufficient**to prove ...Page 1684

Hence , it is quite

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 ...### 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