## Linear Operators, Part 2 |

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Page 1178

( x Then K maps scalar -

( x Then K maps scalar -

**valued**functions into functions with values in ly . It is plain from Plancherel's theorem that X is a bounded mapping of the space L , of scalar -**valued**functions into the space L2 ( 12 ) of square - integrable ...Page 1179

-0 By Plancherel's theorem , L is a bounded mapping of L2 ( 12 ) into the space of scalar -

-0 By Plancherel's theorem , L is a bounded mapping of L2 ( 12 ) into the space of scalar -

**valued**functions ly . Thus , by Corollary 19 and Corollary 17 , L is a bounded mapping of L , ( 12 ) into Ly . It is clear from ( 63 ) and ( 61 ) ...Page 1751

res> k = 0 differentiable m - vector

res> k = 0 differentiable m - vector

**valued**functions defined in C. Similarly , © ( C ) and Ĉ ( C ) will denote the subspaces of Ĉ ° ( C ) consisting of all functions which are multiply periodic of period 27 and of all functions which ...### 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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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero