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

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Page 1301

They are clearly linearly

They are clearly linearly

**independent**. If the assertion of the corollary were false , it would follow that t has a boundary value at a which is**independent**of the set A. , ... , An - 1 , and hence has at least n + 1**independent**...Page 1306

The following table gives the number of linearly

The following table gives the number of linearly

**independent**solutions of ( 1-2 ) 0 = 0 square integrable at a or b when I ( 1 ) +0 . There are four possibilities as shown by the discussion above . At a Number of linearly**independent**...Page 1311

The operator T T ( T ) will be an operator obtained from t by the imposition of a set , which may be vacuous , of k linearly

The operator T T ( T ) will be an operator obtained from t by the imposition of a set , which may be vacuous , of k linearly

**independent**boundary conditions B ; ( ) = 0 , i = 1 , ... , k ; i.e. , T is the restriction of T ( T ) ( cf.### 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