## Linear Operators: Spectral operators |

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Results 1-3 of 74

Page 1976

DE SES Then for every bounded Borel scalar function o defined on the spectrum

o ( A ) , the

bounded E - measurable function of s . The

OEB ...

DE SES Then for every bounded Borel scalar function o defined on the spectrum

o ( A ) , the

**integral**( ii ) Som pld ) E ( d ) ; Â ( s ) ) " O ( A ) is an e - essentiallybounded E - measurable function of s . The

**integral**( iii ) ( o ; Â ( s ) ) e ( ds ) ,OEB ...

Page 1990

Here , we shall first be concerned with certain special examples of convolutions

which map H into H , which belong to the algebra A , and which have an

representation in one of the two forms ( 18 ) ( f * P ) ( 8 ) = S 018 – t ) f ( t ) dt , QEH

...

Here , we shall first be concerned with certain special examples of convolutions

which map H into H , which belong to the algebra A , and which have an

**integral**representation in one of the two forms ( 18 ) ( f * P ) ( 8 ) = S 018 – t ) f ( t ) dt , QEH

...

Page 1991

This observation enables us to define the

the preceding remarks show that x * f is d - integrable and since 1 * * f ( t ) \ ( dt ) |

5 | z * | sup | f ( t ) | ( ; RN ) , RN the

This observation enables us to define the

**integral**... and a functional x * in H * ,the preceding remarks show that x * f is d - integrable and since 1 * * f ( t ) \ ( dt ) |

5 | z * | sup | f ( t ) | ( ; RN ) , RN the

**integral**s x * f ( t ) ^ ( dt ) is continuous in x * .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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