## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

### From inside the book

Results 1-3 of 79

Page 1218

If the

and thus the class ... set o containing e and a closed set 8 contained in e with u (

0-8 ) < E. Clearly the

If the

**restrictions**flo , g | 8 are continuous then so is the**restriction**( af + Bg ) o n dand thus the class ... set o containing e and a closed set 8 contained in e with u (

0-8 ) < E. Clearly the

**restriction**of Xe to the complement of 0-8 is continuous .Page 1239

Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T , is the

linearly independent boundary conditions B : ( x ) = 0 , i = 1 , ... , k , and we have ...

Conversely , let T , 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 oflinearly independent boundary conditions B : ( x ) = 0 , i = 1 , ... , k , and we have ...

Page 1471

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

70 , B ( f ) = B.G. ( 1 ) + B2G , ( t ) = 0 , Bi + B 0 , B1 , B2 real , if ı has boundary ...

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

**restriction**T of Ti ( t ) is of the form B ( 1 ) = a_G7 ( 1 ) +02 G2 ( / ) = 0 , aita70 , B ( f ) = B.G. ( 1 ) + B2G , ( t ) = 0 , Bi + B 0 , B1 , B2 real , if ı has boundary ...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

### Common terms and phrases

additive Akad 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 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