## 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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Results 1-3 of 88

Page 1990

for some E - measurable and essentially bounded complex valued function â on

RN Before illustrating the results of the preceding section , we shall examine the

... RN or a complex valued

for some E - measurable and essentially bounded complex valued function â on

RN Before illustrating the results of the preceding section , we shall examine the

... RN or a complex valued

**set function**, defined on a family E ( ) of sets in RN .Page 1993

This is clear if á is the characteristic

combinations of such

view of ( 26 ) the equation ( 24 ) may also be written as 7 ( * q ) = 1 à ( s ) u ( ds )

79 . By the ...

This is clear if á is the characteristic

**function**of a**set**in and , since linearcombinations of such

**functions**are dense in Ê , it holds for all â in Â . Thus inview of ( 26 ) the equation ( 24 ) may also be written as 7 ( * q ) = 1 à ( s ) u ( ds )

79 . By the ...

Page 2029

As an example of a tempered distribution we might mention the function T ,

determined by a bounded finitely additive

sets in RN which includes the open sets ) by the equation ( 48 ) Ty ( Q ) = 9 ( 8 ) v

( ds ) ...

As an example of a tempered distribution we might mention the function T ,

determined by a bounded finitely additive

**set function**v ( defined on some field ofsets in RN which includes the open sets ) by the equation ( 48 ) Ty ( Q ) = 9 ( 8 ) v

( ds ) ...

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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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### Common terms and phrases

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