## Linear Operators: Spectral operators |

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Page 1931

If x is a vector in X , then by an

X - valued function f defined and

that ( $ I – T ' ) f ( $ ) = x , & € D ( f ) . It is clear that , for such an extension , f ...

If x is a vector in X , then by an

**analytic**extension of R ( E ; T ' ) x will be meant anX - valued function f defined and

**analytic**on an open set D ( S ) z p ( T ) and suchthat ( $ I – T ' ) f ( $ ) = x , & € D ( f ) . It is clear that , for such an extension , f ...

Page 1932

Throughout the rest of this section , x ( 5 ) will denote such a maximal extension

of R ( $ ; T ' ) x in all cases when R ( $ ; T ) x has the single valued extension

property . In this case x ( K ) is a single valued

and ...

Throughout the rest of this section , x ( 5 ) will denote such a maximal extension

of R ( $ ; T ' ) x in all cases when R ( $ ; T ) x has the single valued extension

property . In this case x ( K ) is a single valued

**analytic**function with domain p ( x )and ...

Page 2248

Let f be a function

number of exceptional points p , includes a neighborhood of o ( T ) and a

neighborhood of the point at infinity . Suppose that each exceptional point p

satisfies E ...

Let f be a function

**analytic**in a domain U which , when taken together with a finitenumber of exceptional points p , includes a neighborhood of o ( T ) and a

neighborhood of the point at infinity . Suppose that each exceptional point p

satisfies E ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator discrete domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero