## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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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

n - 1 1 = 0 ( 2 ) Throughout this section , Bi , i = 1 , . . . , n , will denote a set of n

linearly independent

exist two n x n matrices dij and Buy such that ( 1 ) B ( A ) = 3 & 1 . 454540 ) + Buf ...

n - 1 1 = 0 ( 2 ) Throughout this section , Bi , i = 1 , . . . , n , will denote a set of n

linearly independent

**boundary**values for 7 . Thus , by Corollary XIII . 2 . 23 , thereexist two n x n matrices dij and Buy such that ( 1 ) B ( A ) = 3 & 1 . 454540 ) + Buf ...

Page 2491

The operators Te are supposed to be defined on an interval ( a , b ) , to have two

condition A ( f ) = 0 for all the operators Te is imposed ; in this way , a family Tc of

self ...

The operators Te are supposed to be defined on an interval ( a , b ) , to have two

**boundary**values at a and no**boundary**values at b . A common**boundary**condition A ( f ) = 0 for all the operators Te is imposed ; in this way , a family Tc of

self ...

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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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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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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