## 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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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 formal differential

operators and sets of

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 2320

We wish to study the resolvent of T ' ; to do this we shall begin by studying the set

of eigenvalues of T . It is convenient to make a certain normalization of the set { B

} of

We wish to study the resolvent of T ' ; to do this we shall begin by studying the set

of eigenvalues of T . It is convenient to make a certain normalization of the set { B

} of

**boundary conditions**at the outset . Suppose that if B is a boundary value ...Page 2371

Birkhoff [ 3 ] showed that if the set of

regularity hypotheses of Section 4 , the eigenvalue expansion of a function f of

bounded variation converges to t { f ( t + 0 ) + f ( t – 0 ) } at an interior point t of the

interval ...

Birkhoff [ 3 ] showed that if the set of

**boundary conditions**is subject to theregularity hypotheses of Section 4 , the eigenvalue expansion of a function f of

bounded variation converges to t { f ( t + 0 ) + f ( t – 0 ) } at an interior point t of the

interval ...

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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