## Linear Operators: Spectral theory |

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Page 1061

Q.E.D. Having proved the basic

the full

. Riesz in an equivalent but technically more convenient form . This is done in ...

Q.E.D. Having proved the basic

**inequality**of M. Riesz , we now proceed to provethe full

**inequality**of Calderón and Zygmund . Our first step is to put the result of M. Riesz in an equivalent but technically more convenient form . This is done in ...

Page 1105

We now pause to sharpen another of the

continuity of the product TS which was noted in the paragraph following Lemma 9

, the continuity of the norm function which follows from the triangle

Lemma ...

We now pause to sharpen another of the

**inequalities**of Lemma 9 . ... thecontinuity of the product TS which was noted in the paragraph following Lemma 9

, the continuity of the norm function which follows from the triangle

**inequality**ofLemma ...

Page 1173

... manner be identified with the Lo - space on the product set E " XS and the

selle SS 1 / ( , 8 ) | Pdrds . This

... manner be identified with the Lo - space on the product set E " XS and the

**inequality**to be proved reduces to ( 41 ) SoS . 2 ( x - y ) \ x - y " fly , s ) dy dxds Enselle SS 1 / ( , 8 ) | Pdrds . This

**inequality**is nothing but an integrated form of the ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### Common terms and phrases

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 function f 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 satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero