## Linear operators: Spectral operators |

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Page 2307

The last example above illustrates a problem which will be of great concern to us

in the remainder of this chapter: the problem of finding which

The last example above illustrates a problem which will be of great concern to us

in the remainder of this chapter: the problem of finding which

**formal differential****operators**and sets of boundary conditions lead to spectral operators. As our ...Page 2318

Spectral operators Nelson Dunford, Jacob T. Schwartz ... Let T be the unbounded

operator in Hilbert space defined by the

and the boundary conditions [*] /(0)-fc0/'(0)=0, f(l)-k1f'(l)=0, where k0 and kr are ...

Spectral operators Nelson Dunford, Jacob T. Schwartz ... Let T be the unbounded

operator in Hilbert space defined by the

**formal differential operator**t = —(djdx)2and the boundary conditions [*] /(0)-fc0/'(0)=0, f(l)-k1f'(l)=0, where k0 and kr are ...

Page 2371

... were continued by Tamarkin [3], who studied a considerably generalized

problem for nth order differential operators, ... case in which linear conditions are

imposed at interior points of the interval of definition of a

... were continued by Tamarkin [3], who studied a considerably generalized

problem for nth order differential operators, ... case in which linear conditions are

imposed at interior points of the interval of definition of a

**formal differential****operator**.### What people are saying - Write a review

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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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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