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

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Page 1983

Since every s belongs to one of the sets Si , we have 1 - M - 1 S K for every pair ,

u of distinct

operator of type p - 1 . Q . E . D . 14 COROLLARY . Let A be in AP and let S be a ...

Since every s belongs to one of the sets Si , we have 1 - M - 1 S K for every pair ,

u of distinct

**eigenvalues**of Â ( s ) , and Corollary 7 shows that A is a spectraloperator of type p - 1 . Q . E . D . 14 COROLLARY . Let A be in AP and let S be a ...

Page 2131

272 ] ) that the

multiplicity one ; if this point spectrum contains an isolated point , then these

pole of ...

272 ] ) that the

**eigenvalues**on the unit circle are cyclically located and each hasmultiplicity one ; if this point spectrum contains an isolated point , then these

**eigenvalues**are the nth roots of unity for some n . If one such**eigenvalue**is apole of ...

Page 2373

These boundary conditions determine discrete differential operators having

of a ...

These boundary conditions determine discrete differential operators having

**eigenvalues**1 = determined by equations of the form sin 8 = ks . In this case the**eigenvalues**are located asymptotically at the points an ? + ibn In nt . . . , the ratioof a ...

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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