## Linear Operators: Spectral theory |

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Page 1226

Proof . Part ( a )

b ) that any symmetric operator with dense domain has a unique minimal closed

...

Proof . Part ( a )

**follows immediately**from Lemma 5 ( b ) , and part ( b )**follows****immediately**from part ( a ) and Lemma 5 ( c ) . Q . E . D . It follows from Lemma 6 (b ) that any symmetric operator with dense domain has a unique minimal closed

...

Page 1469

Nelson Dunford, Jacob T. Schwartz. from the restriction of 1 to [ a , c ] by

imposition of the boundary conditions f ( a ) = f ( c ) = 0 has no eigenvalues below

2 - 8 / 2 . It

f ...

Nelson Dunford, Jacob T. Schwartz. from the restriction of 1 to [ a , c ] by

imposition of the boundary conditions f ( a ) = f ( c ) = 0 has no eigenvalues below

2 - 8 / 2 . It

**follows immediately**from Theorems 4 . 1 , 4 . 2 , and XII . 7 . 2 that ( T ) ,f ...

Page 1478

The uniqueness of on

, eigenfunctions belonging to distinct eigenvalues have different numbers of

zeros , and since by Corollary 44 this number increases with n , on has at least n

- 1 ...

The uniqueness of on

**follows immediately**from Lemma 41 . Since , by Lemma 45, eigenfunctions belonging to distinct eigenvalues have different numbers of

zeros , and since by Corollary 44 this number increases with n , on has at least n

- 1 ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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