## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 76

Page 898

If we put E ( d ) = 0 when do oT ) is void , then

If we put E ( d ) = 0 when do oT ) is void , then

**Corollary**4 follows immediately from Theorem 1 and**Corollary**IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associated , in**Corollary**4 , with the normal operator ...Page 1301

Q.E.D. WON Talues tired DIELEN proto 23

Q.E.D. WON Talues tired DIELEN proto 23

**COROLLARY**. Lett be a formal differential operator of order n on an interval I with end points a , b , and suppose that the end point a is fixed . Then the functionals A ; ( 1 ) = f ( i ( a ) ...Page 1459

Q.E.D. 400 arbe 30

Q.E.D. 400 arbe 30

**COROLLARY**. A formally positive formally symmetric formal differential operator r is finite below zero . PROOF . It is obvious from Definition 20 that t is bounded below . Thus the present**corollary**follows from ...### 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