## Linear Operators, Part 2 |

### From inside the book

Results 1-3 of 74

Page 1241

then , letting zn = Xn - Yn , we have limn _ n = 0 and limm . n - 7002m - 2n + = 0 .

Moreover , given a > 0 there is an integer N such that if m , n > N , then 12m — %

1 + < ε .

then , letting zn = Xn - Yn , we have limn _ n = 0 and limm . n - 7002m - 2n + = 0 .

**Consequently**there is a number M such that 12m1 + SM , m = 1 , 2 , . . . .Moreover , given a > 0 there is an integer N such that if m , n > N , then 12m — %

1 + < ε .

Page 1383

With boundary conditions A , the eigenvalues are

from the equation sin vă = 0 .

the numbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + ] ) a } ? , n 2

...

With boundary conditions A , the eigenvalues are

**consequently**to be determinedfrom the equation sin vă = 0 .

**Consequently**, in Case A , the eigenvalues 2 arethe numbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + ] ) a } ? , n 2

...

Page 1387

If Il > 0 , the linear combination eivāt = cos Vat + i sin Vat belongs to L2 ( 0 , 0 ) ; if

In < 0 , the linear combination p - ivāt = cos Vīt - i sin Vīt belongs to L , ( 0 , 0 ) .

...

If Il > 0 , the linear combination eivāt = cos Vat + i sin Vat belongs to L2 ( 0 , 0 ) ; if

In < 0 , the linear combination p - ivāt = cos Vīt - i sin Vīt belongs to L , ( 0 , 0 ) .

**Consequently**, by Theorem 3 . 16 , the resolvent R ( 2 ; T ) is an integral operator...

### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

57 other sections not shown

### Other editions - View all

### 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 derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero