## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 79

Page 1239

iency dary Conversely , let 1 , be a self adjoint

iency dary Conversely , let 1 , be a self adjoint

**extension**of T. Then by Lemma 26 , T , is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B. ( x ) = 0 ...Page 1270

**Extensions**of symmetric operators . The problem of determining whether a given symmetric operator has a self adjoint**extension**is of crucial importance in determining whether the spectral theorem may be employed .Page 1397

Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points of the spectrum of a self adjoint

Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points of the spectrum of a self adjoint

**extension**T of To ( t ) is independent of the particular**extension**chosen , i.e. , is independent of the particular ...### 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

### 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