## 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 ( $ ) = c , $ e D ( f ) . It is clear that , for such an extension , f ...

If x is a vector in X , then by an

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

**analytic**on an open set D ( f ) 2 P ( T ) and suchthat ( $ I – T ) f ( $ ) = c , $ e D ( f ) . It is clear that , for such an extension , f ...

Page 1932

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

of R ( Ě ; T ) x in all cases when RTÉ ; T ) , has the single valued extension

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

and ...

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

of R ( Ě ; T ) x in all cases when RTÉ ; T ) , has the single valued extension

property . In this case x ( Á ) 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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