## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 74

Page 2017

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. and the

fraction in the

1681 s } 1 / 2 which is bounded on all of R " . Thus As has a resolution of the

identity .

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. and the

fraction in the

**inequality**( i ) of Theorem 6 is Isi - s2l2 + 2 | 818212 { ( si - 2 ) +1681 s } 1 / 2 which is bounded on all of R " . Thus As has a resolution of the

identity .

Page 2190

Thus for some constant K we have $ ( f ) SK \ f and to prove the final

the present theorem it will suffice to prove that Ife SS ( $ ) . Since both terms in

this

Thus for some constant K we have $ ( f ) SK \ f and to prove the final

**inequality**ofthe present theorem it will suffice to prove that Ife SS ( $ ) . Since both terms in

this

**inequality**are continuous functions of f , it will suffice to prove it for every ...Page 2403

First we shall prove an

is elementary in the sense that it relates only to the norms of the integral kernels

involved . We then use this

First we shall prove an

**inequality**for integral operators ( Lemma 5 below ) whichis elementary in the sense that it relates only to the norms of the integral kernels

involved . We then use this

**inequality**to apply Theorem 1 in an illustrative but ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

### Other editions - View all

### 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 defined Definition denote dense determined differential operator discrete domain elements equation equivalent established 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 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