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

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Page 2068

It is clear that the linear space Lo = Lyn L.

C of all integrable functions which coincide almost everywhere with a continuous

function clearly

It is clear that the linear space Lo = Lyn L.

**satisfies**( 11 ) . Also the space Lo = L ,C of all integrable functions which coincide almost everywhere with a continuous

function clearly

**satisfies**( 11 ) . Example 11.12 shows that the space Lo = Lin L ...Page 2112

The proof of this theorem is based on an analysis of certain B - spaces of vector

valued analytic functions . We say that T

set U and every sequence { fn } of analytic functions from U to X and X e X such ...

The proof of this theorem is based on an analysis of certain B - spaces of vector

valued analytic functions . We say that T

**satisfies**condition ( B ) if for every openset U and every sequence { fn } of analytic functions from U to X and X e X such ...

Page 2399

Let the hypotheses of Corollary 2 be satisfied . Then the equation to = 0 has two

solutions 0 , and on satisfying the asymptotic relationships oi ( t ) ~ 1 , 02 ( t ) ~ t

as t → 00 . PROOF . We saw in Corollary 2 that oz ( t ) = 0 ( t , 0 )

...

Let the hypotheses of Corollary 2 be satisfied . Then the equation to = 0 has two

solutions 0 , and on satisfying the asymptotic relationships oi ( t ) ~ 1 , 02 ( t ) ~ t

as t → 00 . PROOF . We saw in Corollary 2 that oz ( t ) = 0 ( t , 0 )

**satisfies**the first...

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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