## Linear Operators: Spectral operators |

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This will give analytic conditions on an operator which are sufficient to insure that

it is a spectral operator . The basic ... The next two sections deal with applications

of this main result to non - symmetric ordinary

This will give analytic conditions on an operator which are sufficient to insure that

it is a spectral operator . The basic ... The next two sections deal with applications

of this main result to non - symmetric ordinary

**differential operators**. We let the ...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

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 2318

7 , 1 - BO ) n = m has a finite dimensional range for all sufficiently large m , and

hence , a fortiori , E . has a finite dimensional range . Q . E . D . + 11 THEOREM .

Let T be the unbounded

7 , 1 - BO ) n = m has a finite dimensional range for all sufficiently large m , and

hence , a fortiori , E . has a finite dimensional range . Q . E . D . + 11 THEOREM .

Let T be the unbounded

**operator**in Hilbert space defined by the formal**differential**...### What people are saying - Write a review

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algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete consider constant contained 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero