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

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Results 1-3 of 74

Page 1915

This was possible since it concerns a type of operator with a number of special

properties including first order rate of growth of the

Thus the reader whose primary interest is in the applications to such topics as ...

This was possible since it concerns a type of operator with a number of special

properties including first order rate of growth of the

**resolvent**near the spectrum .Thus the reader whose primary interest is in the applications to such topics as ...

Page 1931

... shall refer to the resolution of the identity for T . In the discussion of spectral

operators we shall encounter a new notion , namely , that of an analytic extension

of RTÉ ; T ) x . Here and elsewhere the symbol R ( $ ; T ) is used for the

...

... shall refer to the resolution of the identity for T . In the discussion of spectral

operators we shall encounter a new notion , namely , that of an analytic extension

of RTÉ ; T ) x . Here and elsewhere the symbol R ( $ ; T ) is used for the

**resolvent**...

Page 2590

2 ( 1930 ) for an operator , condition for , XV . 15 . 35 ( 2079 ) definition of , XV . 3 .

9 ( 1936 ) existence of , XV . 3 . 8 ( 1935 ) non - vanishing on open sets , XV . 15 .

15 ( 2076 ) uniqueness of , XV . 3 . 8 ( 1935 )

2 ( 1930 ) for an operator , condition for , XV . 15 . 35 ( 2079 ) definition of , XV . 3 .

9 ( 1936 ) existence of , XV . 3 . 8 ( 1935 ) non - vanishing on open sets , XV . 15 .

15 ( 2076 ) uniqueness of , XV . 3 . 8 ( 1935 )

**Resolvent**, of a spectral operator ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex 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 statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero