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

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Page 2011

For every set o in & and every such matrix Â ( 8 ) we

= Â ( 8 ) , 8€0 , = 0 , 80 , and the operator Âg in HP according to the ... It is clear

that for such sets o the operator Â , is a bounded everywhere

For every set o in & and every such matrix Â ( 8 ) we

**define**the matrix ( 1 ) Â ( 8 )= Â ( 8 ) , 8€0 , = 0 , 80 , and the operator Âg in HP according to the ... It is clear

that for such sets o the operator Â , is a bounded everywhere

**defined**operator .Page 2018

in the notation for the natural closed extension As , for in this case the symbol A is

used for the restriction As to O , that is , the formal differential operator which

...

in the notation for the natural closed extension As , for in this case the symbol A is

used for the restriction As to O , that is , the formal differential operator which

**defines**As . The spectra of the unbounded operators we have been discussing in...

Page 2284

As the measures My are finite , W , is

W T , is a densely

inverse . We suppose the norm of [ h1 , . . . , hn ] in Hn is

Se ...

As the measures My are finite , W , is

**defined**and continuous , and the map An =W T , is a densely

**defined**closed map of En X into Hn with densely**defined**inverse . We suppose the norm of [ h1 , . . . , hn ] in Hn is

**defined**to be 11 / 2 ( ÈSe ...

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous 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 perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero