## Linear Operators: Spectral operators |

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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 2320

We wish to study the resolvent of T ; to do this we shall begin by studying the set

of eigenvalues of T . It is convenient to make a certain normalization of the set { B

} of

We wish to study the resolvent of T ; to do this we shall begin by studying the set

of eigenvalues of T . It is convenient to make a certain normalization of the set { B

} of

**boundary conditions**at the outset . Suppose that if B is a boundary value ...Page 2345

and a simple computation based on the condition given in Regularity Hypothesis

1 shows that such a set of

Thus a set of two linearly independent

and a simple computation based on the condition given in Regularity Hypothesis

1 shows that such a set of

**boundary conditions**is regular if and only if k + k ' # 0 .Thus a set of two linearly independent

**boundary conditions**for the second ...### 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