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

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Results 1-3 of 67

Page 2286

If A is the closed densely defined linear map of X into the Hilbert space H of

Lemma 35 , then the closure of AQA - 1 is a bounded normal operator . For each

bounded Borel function g on the plane let Š ( g )

1 .

If A is the closed densely defined linear map of X into the Hilbert space H of

Lemma 35 , then the closure of AQA - 1 is a bounded normal operator . For each

bounded Borel function g on the plane let Š ( g )

**denote**the closure of AS ( 9 ) A -1 .

Page 2320

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. n - 1 n - 1 j = 0 Throughout this section , Bi , i = 1 , n , will

...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. n - 1 n - 1 j = 0 Throughout this section , Bi , i = 1 , n , will

**denote**a set of n linearly independent boundary values for 7. Thus , by Corollary...

Page 2436

Next , let C ( En )

valued functions defined in En and vanishing outside a bounded set , let g EC (

EM ) , and let g = f , with f e L ( En ) , so that , by the Plancherel theorem ( XV.11.3

) , we ...

Next , let C ( En )

**denote**the set of all infinitely often differentiable complexvalued functions defined in En and vanishing outside a bounded set , let g EC (

EM ) , and let g = f , with f e L ( En ) , so that , by the Plancherel theorem ( XV.11.3

) , we ...

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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