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

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Page 1297

Q.E.D. We now turn to a discussion of the specific form assumed in the present case by the abstract "

Q.E.D. We now turn to a discussion of the specific form assumed in the present case by the abstract "

**boundary values**" introduced in the last chapter . We shall see that the discussion leads us to a number of results about deficiency ...Page 1305

If B ( 1 ) O is not a boundary condition either at a or at b ( so that , by Theorem 19 , the equation B ( A ) = 0 may be written as B. ( t ) = B2 ( 1 ) , where B , and B , are non - zero

If B ( 1 ) O is not a boundary condition either at a or at b ( so that , by Theorem 19 , the equation B ( A ) = 0 may be written as B. ( t ) = B2 ( 1 ) , where B , and B , are non - zero

**boundary values**at a and b respectively ) ...Page 1307

**boundary values**C ,, C2 , D1 , D , where C1 , C , are**boundary values**at a and D. , D , are**boundary values**at b , such that ( 7 ) ... so the functional A defined by the formula Ā ( f ) = A ( 5 ) is also a**boundary value**for t .### 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