## Linear Operators: Spectral theory |

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Results 1-3 of 73

Page 1027

... the operator ET / ( T ) to the finite dimensional space EH . PROOF . ( a ) Since

H is infinite dimensional the origin

Suppose that a 70

VII .

... the operator ET / ( T ) to the finite dimensional space EH . PROOF . ( a ) Since

H is infinite dimensional the origin

**belongs**to the spectrum of both T and ET .Suppose that a 70

**belongs**to the spectrum of T . Since T is compact , TheoremVII .

Page 1116

1 , B

plainly self adjoint and A

= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA

1 , B

**belongs**to the Hilbert - Schmidt class Cz . If we let Aq ; = ri - P2Pi , then A isplainly self adjoint and A

**belongs**to the class Cr , where r ( 1 - p / 2 ) = p , i . e . , r= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA

**belongs**to the class Cs , where s ...Page 1684

Then , if every partial derivative of F of order k

every partial derivative of F of order not more than m is continuous in the closure

of Em . PROOF . By Corollary 2 and Hölder ' s inequality , each ( k - m ) th ...

Then , if every partial derivative of F of order k

**belongs**to L ( Em ) , it follows thatevery partial derivative of F of order not more than m is continuous in the closure

of Em . PROOF . By Corollary 2 and Hölder ' s inequality , each ( k - m ) th ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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