## Linear Operators: Spectral theory |

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Page 1164

The general inequalities of Section 7 are due to Calderón and Zygmund [ 1 ] and

[ 5 ] ; the particular case n = 1 ( Hilbert transform ) to M . Riesz . Calderón and

Zygmund [ 1 ] show that if the function 2

continuity ...

The general inequalities of Section 7 are due to Calderón and Zygmund [ 1 ] and

[ 5 ] ; the particular case n = 1 ( Hilbert transform ) to M . Riesz . Calderón and

Zygmund [ 1 ] show that if the function 2

**satisfies**a suitable , rather weak ,continuity ...

Page 1385

The function e - V - 12

if 1 - kv - = 0 ; i . e . , if and only if k is positive and a = - 1 / ko . Thus , only in case (

iv ) does Tk have a non - void point spectrum , which consists of the single ...

The function e - V - 12

**satisfies**the boundary condition f ( 0 ) + kf ' ( 0 ) if and onlyif 1 - kv - = 0 ; i . e . , if and only if k is positive and a = - 1 / ko . Thus , only in case (

iv ) does Tk have a non - void point spectrum , which consists of the single ...

Page 1705

... to

is in A ( m ) ( I ) ; here Lemma 3 . 6 ( iv ) permits the use of the Leibniz formula to

show that alt89 ) = qo08€ + g ( J , ε ) for JI Sp , where , by Lemmas 3 . 22 and 3 .

... to

**satisfies**the partial differential equation aj ( ex ) ( VEP ) = če , JI = P where ĝsis in A ( m ) ( I ) ; here Lemma 3 . 6 ( iv ) permits the use of the Leibniz formula to

show that alt89 ) = qo08€ + g ( J , ε ) for JI Sp , where , by Lemmas 3 . 22 and 3 .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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