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

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Page 2103

This Wiener theorem and P . Lévy ' s generalization

by any function f ( a ) analytic for å in a neighborhood of the spectrum of the

element a in A , are extensions of the results to be found in IX . 4 . 10 and IX . 4 .

11 .

This Wiener theorem and P . Lévy ' s generalization

**obtained**by replacing 1 / 2by any function f ( a ) analytic for å in a neighborhood of the spectrum of the

element a in A , are extensions of the results to be found in IX . 4 . 10 and IX . 4 .

11 .

Page 2176

( T ) can be dropped and analogous results

certain types of operational calculi , although their assumptions were quite

different in ...

( T ) can be dropped and analogous results

**obtained**. Similar results were also**obtained**by Dollinger [ 1 ] and Sine [ 1 ] under the hypothesis that T satisfiescertain types of operational calculi , although their assumptions were quite

different in ...

Page 2405

The same conclusion is readily

to the reader to give the necessary details . Next let 1 srs 2 . Let hy be a second

non - negative , u - measurable function defined on S . Then we conclude as ...

The same conclusion is readily

**obtained**in the extreme case r = 00 ; we leave itto the reader to give the necessary details . Next let 1 srs 2 . Let hy be a second

non - negative , u - measurable function defined on S . Then we conclude as ...

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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