## Linear Operators: Spectral theory |

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Page 1301

They are clearly linearly

it would follow that i has a boundary value at a which is

, . . . , An - 1 , and hence has at least n + 1

They are clearly linearly

**independent**. If the assertion of the corollary were false ,it would follow that i has a boundary value at a which is

**independent**of the set A ., . . . , An - 1 , and hence has at least n + 1

**independent**boundary values at a .Page 1306

The following table gives the number of linearly

= 0 square integrable at a or b when I ( 2 ) # 0 . There are four possibilities as

shown by the discussion above . Number of linearly

square ...

The following table gives the number of linearly

**independent**solutions of ( T - ) 0= 0 square integrable at a or b when I ( 2 ) # 0 . There are four possibilities as

shown by the discussion above . Number of linearly

**independent**solutionssquare ...

Page 1311

The operator T = T ( T ) will be an operator obtained from t by the imposition of a

set , which may be vacuous , of k linearly

) = 0 , i = 1 , . . . , k ; i . e . , T is the restriction of T ( T ) ( cf . Definition 2 . 8 ) to the ...

The operator T = T ( T ) will be an operator obtained from t by the imposition of a

set , which may be vacuous , of k linearly

**independent**boundary conditions B ; ( 1) = 0 , i = 1 , . . . , k ; i . e . , T is the restriction of T ( T ) ( cf . Definition 2 . 8 ) to the ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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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