## Linear Operators: Spectral theory |

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Page 1241

Nelson Dunford, Jacob T. Schwartz. then , letting 2n = Xn - Yn , we have limn -

700 ? n = 0 and limm , n - 702m — znl + = 0 .

such that 12m1 + SM , m = 1 , 2 , . . . . Moreover , given ε > 0 there is an integer N

...

Nelson Dunford, Jacob T. Schwartz. then , letting 2n = Xn - Yn , we have limn -

700 ? n = 0 and limm , n - 702m — znl + = 0 .

**Consequently**there is a number Msuch that 12m1 + SM , m = 1 , 2 , . . . . Moreover , given ε > 0 there is an integer N

...

Page 1383

With boundary conditions A , the eigenvalues are

from the equation sin vă = 0 .

the numbers of the form ( na ) , n 21 ; in Case C , the numbers { ( n + 3 ) a } ? , n ...

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 21 ; in Case C , the numbers { ( n + 3 ) a } ? , n ...

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...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 |

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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 consider 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 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