## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 76

Page 1343

Thus E ( M ( 2 ) ; U ) is non - zero for a near ho , de 0o , and it follows that for a

number of distinct points in the spectrum of M ( a ) , the sets { 2 € o ln ( 2 ) 2 s } are

...

Thus E ( M ( 2 ) ; U ) is non - zero for a near ho , de 0o , and it follows that for a

**sufficiently**close to 20 , 0 ( M ( 2 ) ) U is non - void . Thus if n ( a ) denotes thenumber of distinct points in the spectrum of M ( a ) , the sets { 2 € o ln ( 2 ) 2 s } are

...

Page 1440

... ( T ) ) if c is

Theorem 4 to a

DIFFERENTIAL OPERATORS XIII .

... ( T ) ) if c is

**sufficiently**large . Let 2o be real and positive . Passing by means ofTheorem 4 to a

**sufficiently**small subinterval [ ao , b ) of ( a 1440 ORDINARYDIFFERENTIAL OPERATORS XIII .

Page 1449

Nelson Dunford, Jacob T. Schwartz. for ao

< oo for a ,

monotone decreasing for

( t ) ...

Nelson Dunford, Jacob T. Schwartz. for ao

**sufficiently**large , and if 19 ( t ) 1 - 42dt< oo for a ,

**sufficiently**large , then oe ( T ) is void . ( d ) If g ( t ) → - 00 , if q ismonotone decreasing for

**sufficiently**large t , if 1 / 9 ( t ) ' \ _ 1 ( 9 ( t ) ' ) ? | - dt < 19( t ) ...

### What people are saying - Write a review

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

### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### Other editions - View all

### Common terms and phrases

additive 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 differential equations domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 Proc projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero