## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 58

Page 1051

Statement ( i ) is

consequences of Definition 1 and of the formulae Sen 9 ( x ) dx = Sem P ( Ux ) dx

, Sen g ( xx ) dx = ( 2xl - srn9 ( x ) dx , which are valid for every Lebesgue ...

Statement ( i ) is

**evident**from Definition 1 . Statements ( ii ) and ( iii ) are**evident**consequences of Definition 1 and of the formulae Sen 9 ( x ) dx = Sem P ( Ux ) dx

, Sen g ( xx ) dx = ( 2xl - srn9 ( x ) dx , which are valid for every Lebesgue ...

Page 1631

... A → be the mapping which assigns to every set [ go , . . . , & m - 1 ] of data the

corresponding unique solutions of the equation Lf = 0 . It is

, and equally

... A → be the mapping which assigns to every set [ go , . . . , & m - 1 ] of data the

corresponding unique solutions of the equation Lf = 0 . It is

**evident**that T is linear, and equally

**evident**that T is closed . Hence , by the closed graph theorem ( 11 .Page 1756

( B ) The uniqueness of the function V of the theorem is an

of statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the

existence of the function V to the proof of the following statement . ( ii ) For each r

...

( B ) The uniqueness of the function V of the theorem is an

**evident**consequenceof statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the

existence of the function V to the proof of the following statement . ( ii ) For each r

...

### What people are saying - Write a review

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

### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero