## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 72

Page 1436

... { n }

elements of D ( T ) such that { Tgn }

} such that x * ( hi )

is ...

... { n }

**converges**, then { { n }**converges**. Let { 8n } be a bounded sequence ofelements of D ( T ) such that { Tgn }

**converges**. Find a subsequence { gn , } = { h ;} such that x * ( hi )

**converges**for each ; , 1 si s k . Then ñ ; = h ; - * * - * * ( h ; ) q ;is ...

Page 1461

If this is false , then by Corollary 2 there exists a bounded sequence { m } of D ( T .

( 7 + t , ) ) such that { ( t + titute ) fm }

convergent subsequence . Let 8m = P / m . Then { 8m } is a bounded sequence in

the ...

If this is false , then by Corollary 2 there exists a bounded sequence { m } of D ( T .

( 7 + t , ) ) such that { ( t + titute ) fm }

**converges**, but such that { fm } has noconvergent subsequence . Let 8m = P / m . Then { 8m } is a bounded sequence in

the ...

Page 1664

The Fourier series of an element F in D , ( C )

Proof . It follows from the Definition 37 of the topology in D , ( C ) that it suffices to

show that ( 27 ) * { F25 cil 3g ( a ) de

q ...

The Fourier series of an element F in D , ( C )

**converges**unconditionally to F .Proof . It follows from the Definition 37 of the topology in D , ( C ) that it suffices to

show that ( 27 ) * { F25 cil 3g ( a ) de

**converges**unconditionally to F ( P ) for eachq ...

### 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