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

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Page 1217

Two ordered representations U and Ū of H relative to T and †

Two ordered representations U and Ū of H relative to T and †

**respectively**, with measures u and ủ , and multiplicity sets { en } and { ēn } will be called M equivalent if u and ( e , děn ) = 0 = ùle , 4ěn ) for n = 1 , 2 , ....Page 1302

Corollary 23 and from Theorems 19 and 20 that d ' and d ' exceed by n the number of independent boundary values at a and at b

Corollary 23 and from Theorems 19 and 20 that d ' and d ' exceed by n the number of independent boundary values at a and at b

**respectively**. The statement of the present corollary is then evident . Q.E.D. + 26 COROLLARY .Page 1548

n 1 2 τ extensions of S and Ŝ

n 1 2 τ extensions of S and Ŝ

**respectively**, and let 2 , ( T ) and an ( Î ) be the numbers defined for the self adjoint operators T and Î as in Exercise D2 . Show that 2 ( T ) 2 an ( ) , n 2 1 . Dil Let Tį be a self adjoint operator in ...### 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 Ly(R 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 unique unit unitary vanishes vector zero