## Linear Operators: Spectral theory |

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Page 1099

... approximated arbitrarily closely by non -

consider the case in which T is non -

.

... approximated arbitrarily closely by non -

**singular**matrices , it is sufficient toconsider the case in which T is non -

**singular**. Then A = ( TT * ) 1 / 2 is also non -**singular**and if U = A - 17 , UU * = A - 1 A2A - 1 = 1 , then U is unitary , and T = AU.

Page 1184

These B - spaces have been studied extensively in connection with the theory of

shown under suitable hypotheses to map functions satisfying a Hölder condition

...

These B - spaces have been studied extensively in connection with the theory of

**singular**integrals .**Singular**integrals of Hilbert - CalderónZygmund type may beshown under suitable hypotheses to map functions satisfying a Hölder condition

...

Page 1919

7 ( 136 )

258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (

160 – 162 ) , IV . 2 . 15 - 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 – 390 )

study ...

7 ( 136 )

**singular**, III . 4 . 12 ( 131 ) spaces of , as conjugate spaces , IV . 5 . 1 (258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (

160 – 162 ) , IV . 2 . 15 - 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 – 390 )

study ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

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### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero