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

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Page 1321

The matrices l ' = ( y ) and I ' = ( ) in the Vis Vís preceding theorem are uniquely

The matrices l ' = ( y ) and I ' = ( ) in the Vis Vís preceding theorem are uniquely

**determined**by the jump equations and by the boundary conditions defining T. 9 PROOF . We have seen in the derivation of Theorem 8 that the functions ai ...Page 1323

To

To

**determine**the u * + v * = ( p * + q * ) - ( u * + v * ) = + ( n + k * ) - ( u * + v * ) numbers a ; ( t ) and Bi ( t ) ... Thus ( Vis ) and ( ii ) are uniquely**determined**by the jump conditions and by the boundary conditions E * ( K ) ...Page 1497

Let the eigenvalues

Let the eigenvalues

**determined**by the periodic boundary conditions stated above be enumerated in increasing order , and repeated according to multiplicity , be Po , P1 , P2 , ... , . Let the corresponding enumeration of the eigenvalues ...### 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