## Linear Operators: Spectral operators |

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Results 1-3 of 73

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

... usefulness in the theory of partial differential equations . 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

...

... usefulness in the theory of partial differential equations . 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...

Page 1991

This observation enables us to define the

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

= | z * sup | f ( 0 ) | v ( ; 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 l - integrable and since 1 x * f ( t ) \ ( dt ) |

= | z * sup | f ( 0 ) | v ( ; RN ) , RN the

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

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm 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 uniform uniformly unique valued vector weakly zero