## 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 formal

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 formal

= 0 , f ( 1 ) – ka 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 , f ( 1 ) – ka f ' ( 1 ) = 0 , where ko and ky are arbitrary , possibly infinite ,

complex ...

Page 2371

Investigations along the lines initiated by Birkhoff and Tamarkin were continued

by Tamarkin ( 3 ) , who studied a considerably generalized problem for nth order

...

Investigations along the lines initiated by Birkhoff and Tamarkin were continued

by Tamarkin ( 3 ) , who studied a considerably generalized problem for nth order

**differential operators**, by Birkhoff and Langer [ 1 ] , who treated the case of a first...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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### 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit 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