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

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Page 1224

1 2 1 2 1 2 2 = 1 > 2 ( b ) If T is

1 2 1 2 1 2 2 = 1 > 2 ( b ) If T is

**symmetric**then every**symmetric**extension T , of Tj ; and , in particular , every self adjoint extension of Tı , satisfies Ti CT , CT CT * Proof . If T , CT , and ye D ( T * ) , then ( x , T * y ) ...Page 1236

A set of boundary conditions B ( x ) = 0 , i = 1 , ... , k , is 0 said to be

A set of boundary conditions B ( x ) = 0 , i = 1 , ... , k , is 0 said to be

**symmetric**if the equations B ; ( x ) = B ... Every closed**symmetric**extension of T is the restriction of 1 * to the subspace of D ( T * ) determined by a ...Page 1272

Maximal

Maximal

**symmetric**operators . If T is a**symmetric**operator with dense domain , then it has proper**symmetric**extensions provided both of its deficiency indices are different from zero . A maximal**symmetric**operator is one which has ...### 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