## Linear Operators: Spectral theory |

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Page 1301

They are clearly linearly

it would follow that t 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 t 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 ( a ) + 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 ( a ) + 0 . There are four possibilities as

shown by the discussion above . Number of linearly

**independent**solutionssquare ...

Page 1311

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. with end

points a , b . The operator T = T ( 1 ) will be an operator obtained from t by the

imposition of a set , which may be vacuous , of k linearly

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. with end

points a , b . The operator T = T ( 1 ) will be an operator obtained from t by the

imposition of a set , which may be vacuous , of k linearly

**independent**boundary ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present 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 unit vanishes vector zero