## Linear Operators: Spectral theory |

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Page 1178

Then K maps scalar -

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 L ( 12 ) of square - integrable ...Page 1179

By Plancherel's theorem , L is a bounded mapping of L2 ( l2 ) into the space of scalar -

By Plancherel's theorem , L is a bounded mapping of L2 ( l2 ) into the space of scalar -

**valued**functions lg . Thus , by Corollary 19 and Corollary 17 , L is a bounded mapping of Ly ( 12 ) into Lg . It is clear from ( 63 ) and ( 61 ) ...Page 1918

... IV.7.6 ( 285 ) , ( 394-397 ) as a space of integrable functions , ( 394-396 ) for unitary groups of operators , XII.6.1 ( 1243 ) of a vector -

... IV.7.6 ( 285 ) , ( 394-397 ) as a space of integrable functions , ( 394-396 ) for unitary groups of operators , XII.6.1 ( 1243 ) of a vector -

**valued**function , ( 196 ) for vector -**valued**integrals , III.11.17 ( 198 ) Resolution of ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives 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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero