## 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

Let T be the unbounded operator in Hilbert space defined by the

) = 0 , $ ( 1 ) — kq f ' ( 1 ) = 0 , where ko and ky are arbitrary , possibly infinite ,

complex ...

Let T be the unbounded operator in Hilbert space defined by the

**formal****differential operator**t = - d / dx ) 2 and the boundary conditions [ * ] f ( 0 ) – ko f ' ( 0) = 0 , $ ( 1 ) — kq f ' ( 1 ) = 0 , where ko and ky are arbitrary , possibly infinite ,

complex ...

Page 2371

... who studied a considerably generalized problem for nth order differential

operators , by Birkhoff and Langer [ 1 ] , who ... case in which linear conditions

are imposed at interior points of the interval of definition of a

... who studied a considerably generalized problem for nth order differential

operators , by Birkhoff and Langer [ 1 ] , who ... 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 | |

31 other sections not shown

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero