## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 77

Page 1223

How are we to choose its

How are we to choose its

**domain**? A natural first guess is to choose as**domain**the collection Dy of all functions with one continuous derivative . If f and g are any two such functions , we have ( iDf , g ) = $ . if " ( 1 ) g ( t ) dt ...Page 1249

Thus PP * is a projection whose range is N = PM , the final

Thus PP * is a projection whose range is N = PM , the final

**domain**of P. To complete the proof it will suffice to show that P * P is a projection if P is a partial isometry . Let x , v E M , the initial**domain**of P. Then the identity ...Page 1669

Let I , be a

Let I , be a

**domain**in E " ?, and let 1 , be a**domain**in En . Let M : 1 +1 , be a mapping of I into I , such that ( a ) M - C is a compact subset of I , whenever C is a compact subset of I2 ; ( b ) ( M ( :) ) , Co ( 11 ) , j = 1 ,.### 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