## Linear Operators: Spectral theory |

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Page 1303

Clearly B ( A ) = 0 for those f which vanish in a

boundary value for ī at a . To prove the converse , let B be a boundary value at a .

Choose a function h in Co ( I ) which is identically equal to one in a

...

Clearly B ( A ) = 0 for those f which vanish in a

**neighborhood**of a . Thus B is aboundary value for ī at a . To prove the converse , let B be a boundary value at a .

Choose a function h in Co ( I ) which is identically equal to one in a

**neighborhood**...

Page 1678

Let ý be a second function in Coo ( I ) such that ♡ ( x ) = 1 for x in a

of K . Then yo - yo vanishes in a

o ...

Let ý be a second function in Coo ( I ) such that ♡ ( x ) = 1 for x in a

**neighborhood**of K . Then yo - yo vanishes in a

**neighborhood**of K C ( F ) , and vanishes in a**neighborhood**of C ( F ) - K since y vanishes in the complement of K . Hence yo -o ...

Page 1734

Let U , C1 , be a bounded

so that there exists a mapping o of U , onto the unit spherical

the origin such that ( i ) q is one - to - one , is infinitely often differentiable , and q ...

Let U , C1 , be a bounded

**neighborhood**of q chosen so small that BU , CE , andso that there exists a mapping o of U , onto the unit spherical

**neighborhood**V ofthe origin such that ( i ) q is one - to - one , is infinitely often differentiable , and q ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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