## 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

But , under the condition that the set of

, this has been established above . Thus , to complete the proof , it suffices to

show that the set of

But , under the condition that the set of

**boundary conditions**C ( Uf ) = 0 is regular, this has been established above . Thus , to complete the proof , it suffices to

show that the set of

**boundary conditions**C / ( Uf ) = 0 , i = 1 , . . . , n , is regular .Page 2371

Birkhoff [ 3 ] showed that if the set of

regularity hypotheses of Section 4 , the eigenvalue expansion of a function f of

bounded variation converges to i { f ( t + 0 ) + f ( t - 0 ) } at an interior point t of the

interval ...

Birkhoff [ 3 ] showed that if the set of

**boundary conditions**is subject to theregularity hypotheses of Section 4 , the eigenvalue expansion of a function f of

bounded variation converges to i { f ( t + 0 ) + f ( t - 0 ) } at an interior point t of the

interval ...

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