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

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Page 1912

exception , used from

concerning approximation of integrable functions by smooth functions . The

exception is Sobolev ' s theorem , which is used only in the proof of a corollary

unessential ...

exception , used from

**Chapter**XIV are elementary self - contained lemmasconcerning approximation of integrable functions by smooth functions . The

exception is Sobolev ' s theorem , which is used only in the proof of a corollary

unessential ...

Page 1915

34 , and then directly to

needed for most of

again that the principal results of

34 , and then directly to

**Chapter**XX , thereby eliminating the involved analysisneeded for most of

**Chapter**XVI and all of the material in**Chapters**... the readeragain that the principal results of

**Chapter**XIII are frequently used in**Chapter**XX .Page 1916

properties of the set of eigenvectors of a perturbed operator . These theorems

make assertions less specific than those obtained in the first sections of

XIX ...

**Chapter**XIX ends with a section which gives results concerning completenessproperties of the set of eigenvectors of a perturbed operator . These theorems

make assertions less specific than those obtained in the first sections of

**Chapter**XIX ...

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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