## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2286

For each bounded Borel function g on the plane let Š ( g )

For each bounded Borel function g on the plane let Š ( g )

**denote**the closure of AS ( 9 ) A - 1 . The correspondence 7 : S ( g ) + Š ( 9 ) preserves the operational calculus and Q = 1 ( da ) , o ( Q ) where 7E ( e ) = f ( e ) , e e B.Page 2320

n - 1 n - 1 j = 0 Throughout this section , Bi , i = 1 , n , will

n - 1 n - 1 j = 0 Throughout this section , Bi , i = 1 , n , will

**denote**a set of n linearly independent boundary values for 7. Thus , by Corollary XIII.2.23 , there exist two n x n matrices dig and Bu , such that ( 1 ) B ...Page 2436

Next , let C ( En )

Next , let C ( En )

**denote**the set of all infinitely often differentiable complex valued functions defined in En and vanishing outside a bounded set , let g EC ( EM ) , and let g = f , with f e L ( En ) , so that , by the Plancherel ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero