## Linear Operators: Spectral theory |

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Page 1179

Theorem 25 remains valid in the full range 1 < p < 0 . a

Theorem 25 remains valid in the full range 1 < p < 0 . a

**PROOF**. We saw in the course of proving Theorem 25 that the mapping MX which sends a scalar - valued function with the Fourier transform f ( ) into the vector - valued function ...Page 1724

0 a

0 a

**Proof**. By the preceding lemma and by Corollary 11 it suffices to show that ( T ) , g ) = ( 1 , Sg ) forf in D ( T ) and g in D ( S ) . By f Green's formula , proved in the last paragraph of Section 2 , this equation is valid if ...Page 1750

We shall see , however , that this fact is needed in the course of the

We shall see , however , that this fact is needed in the course of the

**proof**of Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2. The theorem is false if no boundedness restriction is imposed on the ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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