## Linear Operators: Spectral operators |

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Page 2325

5 and from

16 ) , and

representation 5x ~ 20n + & + za + Smo - m , and that the zero & n of M ( u ) in R 2

...

5 and from

**formulas**( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 ,**formula**(16 ) , and

**formula**( 14 ) , that the zero Én of M ( u ) in Rom has the asymptoticrepresentation 5x ~ 20n + & + za + Smo - m , and that the zero & n of M ( u ) in R 2

...

Page 2330

Since Guis analytic by

and Šm of the contour integral ( 27 ) ( nun – 1 R ( um ; T ) — nun - 1 Gu ) du . By

Lemma 3 , if we take any sufficiently small ε > 0 , and let Om denote the circle with

...

Since Guis analytic by

**formula**( 21 ) , we have only to take the residues at Śmand Šm of the contour integral ( 27 ) ( nun – 1 R ( um ; T ) — nun - 1 Gu ) du . By

Lemma 3 , if we take any sufficiently small ε > 0 , and let Om denote the circle with

...

Page 2340

It follows immediately from

in the form K = 1 ( 55 ) ( B , Guf ) = het ... coefficients a , a ' in the constant terms of

A ( u ) and A ' ( u ) are of course the same constants at ap and bp of

It follows immediately from

**formulas**( 52 ) and ( 34 ) that ( B ; Guf ) can be writtenin the form K = 1 ( 55 ) ( B , Guf ) = het ... coefficients a , a ' in the constant terms of

A ( u ) and A ' ( u ) are of course the same constants at ap and bp of

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