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

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Page 2391

For use in what is to follow we record the formula for R ( a ; T ) obtained in the

proof of

For use in what is to follow we record the formula for R ( a ; T ) obtained in the

proof of

**Lemma**4 and also observe that in constructing the kernel R ( 8 , t ; ) in**Lemma**4 we may replace the particular " second solution " olt , ) constructed in ...Page 2396

Then , by equations ( 22 ) and ( 23 ) of that same proof , | f : ( 0 ) | 5 141-3 { 1 *

1968 ) | ds ) ' + I'S 2460 - bq ( e ) del . e It follows from this formula just as in the

proof of

Then , by equations ( 22 ) and ( 23 ) of that same proof , | f : ( 0 ) | 5 141-3 { 1 *

1968 ) | ds ) ' + I'S 2460 - bq ( e ) del . e It follows from this formula just as in the

proof of

**Lemma**1 ( cf. the paragraph following formula ( 14 ) ) that lim 1f ( t ) = 0 ...Page 2479

regarded as a subspace of the larger space H ' of

plainly H , may be regarded as the restriction to H , of the operator H of

15 ( cf. ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace Hi ,

and ...

regarded as a subspace of the larger space H ' of

**Lemma**15 , while equallyplainly H , may be regarded as the restriction to H , of the operator H of

**Lemma**15 ( cf. ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace Hi ,

and ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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 defined Definition denote dense determined differential operator discrete 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