## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 83

Page 2102

The results of

part are due to Foguel [2], as are most of the results in

spectral properties of T, S, and N. Oberai [2] discussed some of these results for ...

The results of

**Section**7 relating properties of a spectral operator and its scalarpart are due to Foguel [2], as are most of the results in

**Section**8 concerning thespectral properties of T, S, and N. Oberai [2] discussed some of these results for ...

Page 2291

reason, and also because of the special importance of second order operators in

applications, a separate proof of the spectral character of —(djdx)^ (subject to a

set of boundary conditions which make it nonselfadjoint) is given in

reason, and also because of the special importance of second order operators in

applications, a separate proof of the spectral character of —(djdx)^ (subject to a

set of boundary conditions which make it nonselfadjoint) is given in

**Section**3.Page 2376

In the first

successfully if q is of a degree of small - ness conforming with the requirement \" (

I +ta)\q[t)\dt< co. •la The idea involved is of quite general applicability; a number

of other ...

In the first

**section**we shall show that this program can be carried throughsuccessfully if q is of a degree of small - ness conforming with the requirement \" (

I +ta)\q[t)\dt< co. •la The idea involved is of quite general applicability; a number

of other ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero