## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 82

Page 1321

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

The matrices l ' = ( Vis ) 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 ...Page 1323

To

To

**determine**the u * + v * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( u * + v * ) numbers a ; lt ) and Bi ( t ) ... By symmetry ( y is ) and ( y's ) are also**determined**uniquely by the jump conditions and the boundary conditions Ez ...Page 1497

Then by Theorems XII.4.28 , 4.1 , and 4.2 , these sets of boundary conditions

Then by Theorems XII.4.28 , 4.1 , and 4.2 , these sets of boundary conditions

**determine**self adjoint operators T ... Let the eigenvalues**determined**by the periodic boundary conditions stated above be enumerated in increasing order ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

44 other sections not shown

### Other editions - View all

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity 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