## Linear Operators: Spectral theory |

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Page 1178

Then x maps scalar -

from Plancherel ' s theorem that X is a bounded mapping of the space L , of

scalar -

Then x maps scalar -

**valued**functions into functions with values in ls . It is plainfrom Plancherel ' s theorem that X is a bounded mapping of the space L , of

scalar -

**valued**functions into the space L ( 12 ) of square - integrable vector -**valued**...Page 1179

By Plancherel ' s theorem , L is a bounded mapping of L2 ( 12 ) into the space of

scalar -

bounded mapping of L , ( 12 ) into Ly . It is clear from ( 63 ) and ( 61 ) that L M

maps G ...

By Plancherel ' s theorem , L is a bounded mapping of L2 ( 12 ) into the space of

scalar -

**valued**functions lg . Thus , by Corollary 19 and Corollary 17 , L is abounded mapping of L , ( 12 ) into Ly . It is clear from ( 63 ) and ( 61 ) that L M

maps G ...

Page 1751

H = 2 J + isk and differentiable m - vector

, İİo ( C ) and C ( C ) will denote the subspaces of Ĉ ( C ) consisting of all

functions which are multiply periodic of period 2n and of all functions which

vanish ...

H = 2 J + isk and differentiable m - vector

**valued**functions defined in C . Similarly, İİo ( C ) and C ( C ) will denote the subspaces of Ĉ ( C ) consisting of all

functions which are multiply periodic of period 2n and of all functions which

vanish ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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