## Linear Operators: Spectral theory |

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Page 1249

Thus PP * is a projection whose range is N = PM , the final domain of P. To

complete the proof it will suffice to show that P * P is a projection if P is a

isometry . Let x , v € M , the initial domain of P. Then the identity ( x + v12 = \ Px +

Pul2 ...

Thus PP * is a projection whose range is N = PM , the final domain of P. To

complete the proof it will suffice to show that P * P is a projection if P is a

**partial**isometry . Let x , v € M , the initial domain of P. Then the identity ( x + v12 = \ Px +

Pul2 ...

Page 1633

A third category of formal

the operator a 22 ox да , This sort of operator is closely related to the theory of

semi - groups , where we have already seen general equations of the form a T ( t

) ...

A third category of formal

**partial**differential operators is the parabolic , typified bythe operator a 22 ox да , This sort of operator is closely related to the theory of

semi - groups , where we have already seen general equations of the form a T ( t

) ...

Page 1703

The Elliptic Boundary Value Problem Can the boundary value theory and the

spectral theory of Chapter XIII be generalized to

the present section it will be seen that it can , at least for the class of elliptic

...

The Elliptic Boundary Value Problem Can the boundary value theory and the

spectral theory of Chapter XIII be generalized to

**partial**differential operators ? Inthe present section it will be seen that it can , at least for the class of elliptic

**partial**...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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