## Linear Operators: Spectral theory |

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Page 1321

The matrices I = ( Y .; ) and I " = ( yúj ) in the preceding theorem are uniquely

PROOF . We have seen in the derivation of Theorem 8 that the functions & ; ( t )

and Bi ...

The matrices I = ( Y .; ) and I " = ( yúj ) in the preceding theorem are uniquely

**determined**by the jump equations and by the boundary conditions defining T.PROOF . We have seen in the derivation of Theorem 8 that the functions & ; ( t )

and Bi ...

Page 1323

To

numbers a ; ( t ) and Bi ( t ) we have the n jump ... Bie Wg . Thus ( Vis ) and ( Vis )

are uniquely

E * ( K ) ...

To

**determine**the u * + v * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( u * + v * )numbers a ; ( t ) and Bi ( t ) we have the n jump ... Bie Wg . Thus ( Vis ) and ( Vis )

are uniquely

**determined**by the jump conditions and by the boundary conditionsE * ( K ) ...

Page 1497

Let the eigenvalues

above be enumerated in increasing order , and repeated according to multiplicity

, be Po , P1 , P2 , ... , . Let the corresponding enumeration of the eigenvalues ...

Let the eigenvalues

**determined**by the periodic boundary conditions statedabove be enumerated in increasing order , and repeated according to multiplicity

, be Po , P1 , P2 , ... , . Let the corresponding enumeration of the eigenvalues ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero