## 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 5

Page 1983

... all convolution operators in H = L2 ( RN ) , the Hilbert space of

functions , ordinary Lebesgue integrals , proper value integrals or any other

improper integral ...

... all convolution operators in H = L2 ( RN ) , the Hilbert space of

**square****integrable**functions on real Euclidean space RN of ... countably additive setfunctions , ordinary Lebesgue integrals , proper value integrals or any other

improper integral ...

Page 2042

1 ) we have , by differentiating under the integral sign as before , RN RN ( 241o , )

( Q ) = Sxv6 – 1 « la za ( F - 14 ) ... ( s ) in the preceding integrand is

1 ) we have , by differentiating under the integral sign as before , RN RN ( 241o , )

( Q ) = Sxv6 – 1 « la za ( F - 14 ) ... ( s ) in the preceding integrand is

**square****integrable**on RN and the same is true of its Fourier transform F ( ( - 1 ) | a1 ( 2 . ) ...Page 2043

... is continuous on RN and

21 THEOREM . Using the notation of Theorem 19 and letting B be an arbitrary

bounded linear operator in HP , we have : ( i ) The operator As + B with domain D

...

... is continuous on RN and

**square integrable**on RN , then q belongs to D ( A ) .21 THEOREM . Using the notation of Theorem 19 and letting B be an arbitrary

bounded linear operator in HP , we have : ( i ) The operator As + B with domain D

...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero