## 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 2350

U - 1TU is the same as the operator in Hilbert space defined by the formal

differential operator ( - id / dt + b ' ( t ) ) " and the set C : ( Uf ) = 0 , i = 1 . . . n , of

operator Idin ...

U - 1TU is the same as the operator in Hilbert space defined by the formal

differential operator ( - id / dt + b ' ( t ) ) " and the set C : ( Uf ) = 0 , i = 1 . . . n , of

**boundary**conditions . Since ( = in ( l ) + ) * = = ( 3 . ) * + 49 - 196 ) * + . . . , theoperator Idin ...

Page 2517

Birkhoff , G . D . 3 .

differential equations . Trans . Amer . Math . Soc . 9 , 373 – 395 ( 1908 ) . 6 . Note

on the expansion of the Green ' s function . Math . Ann . 72 , 292 – 294 ( 1912 ) . 7

.

Birkhoff , G . D . 3 .

**Boundary**value and expansion problems of ordinary lineardifferential equations . Trans . Amer . Math . Soc . 9 , 373 – 395 ( 1908 ) . 6 . Note

on the expansion of the Green ' s function . Math . Ann . 72 , 292 – 294 ( 1912 ) . 7

.

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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