## Linear Operators: Spectral theory |

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Page 1175

Then K , is a bounded

each real & o , let Ht , be the

( H 5 , 1 ) ( 5 ) = f ( s ) , 5 > 60 , otherwise . = 0 By Corollary 22 , it follows that ...

Then K , is a bounded

**mapping**of the space L ( L , ( S ) ) into itself . PROOF . Foreach real & o , let Ht , be the

**mapping**in La ( L ( S ) ) defined by the formula ( 47 )( H 5 , 1 ) ( 5 ) = f ( s ) , 5 > 60 , otherwise . = 0 By Corollary 22 , it follows that ...

Page 1179

By Plancherel ' s theorem , L is a bounded

scalar - valued functions lg . Thus , by Corollary 19 and Corollary 17 , L is a

bounded

By Plancherel ' s theorem , L is a bounded

**mapping**of L2 ( 12 ) into the space ofscalar - valued functions lg . Thus , by Corollary 19 and Corollary 17 , L is a

bounded

**mapping**of L , ( 12 ) into Ly . It is clear from ( 63 ) and ( 61 ) that L M**maps**G ...Page 1671

But then ( iii ) is evident . Q . E . D . Lemma 47 allows us to describe the behavior

of the spaces HP , AP , etc . , under the changes of variable . 48 LEMMA . Let I ,

and I , be domains in E " , and let M : 14 + 1 , be a one - to - one

But then ( iii ) is evident . Q . E . D . Lemma 47 allows us to describe the behavior

of the spaces HP , AP , etc . , under the changes of variable . 48 LEMMA . Let I ,

and I , be domains in E " , and let M : 14 + 1 , be a one - to - one

**mapping**of I ...### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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