## Linear Operators: Spectral theory |

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Page 1297

We shall also be able to locate

points of the interval , and to represent

form . The fundamental definitions are as follows : 17 DEFINITION . Let ī be a

formal ...

We shall also be able to locate

**boundary values**at one or another of the endpoints of the interval , and to represent

**boundary values**in a concrete analyticalform . The fundamental definitions are as follows : 17 DEFINITION . Let ī be a

formal ...

Page 1298

If I is formally self adjoint , then Definition 17 of a

with Definition XII . 4 . 20 of a

gives a basic property of

of ...

If I is formally self adjoint , then Definition 17 of a

**boundary value**for t coincideswith Definition XII . 4 . 20 of a

**boundary value**for ... Q . E . D . The next theoremgives a basic property of

**boundary values**of differential operators . For the sakeof ...

Page 1307

D1 , D , are

conjugate of the

linear ...

**boundary values**C1 , C2 , D2 , D , where C1 , C , are**boundary values**at a andD1 , D , are

**boundary values**at b , such that ( tt ... We may call it the complexconjugate of the

**boundary value**A . The**boundary value**A may be written as alinear ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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additive Akad 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 domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f 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 Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero