## Linear Operators: Spectral operators |

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Page 2260

(iii') There is a

yo)\ ds ZM\y*\ \y0\, y0ey0,yt e?)*, J<HS2> where s is the arc length along C. We

now note (cf. Theorem VII.9.5 and formula [*] of the proof of Lemma VII.9.2) that ...

(iii') There is a

**constant**M depending only on S such that I* +(A, yt, y0)-B-(\, ye*.yo)\ ds ZM\y*\ \y0\, y0ey0,yt e?)*, J<HS2> where s is the arc length along C. We

now note (cf. Theorem VII.9.5 and formula [*] of the proof of Lemma VII.9.2) that ...

Page 2425

f(o)do, it follows from Lemma 5 and from (31) and (32) that there exists a finite

fi)U\\i.^l l/(*)|2 ^}1/2- On the other hand, it follows from (30) that (35) (r(A)f)[s) ...

f(o)do, it follows from Lemma 5 and from (31) and (32) that there exists a finite

**constant**N(y, [3) depending only on y and /? such that (34) |(JW)(«)|a(fe)1/a <N(y,fi)U\\i.^l l/(*)|2 ^}1/2- On the other hand, it follows from (30) that (35) (r(A)f)[s) ...

Page 2441

This shows that there exists a finite absolute

n + 1. Using this inequality and using (37), we see that there exists a finite

) ...

This shows that there exists a finite absolute

**constant**c' such that I(a)\ ^ c'(l + |a|)_n + 1. Using this inequality and using (37), we see that there exists a finite

**constant**M" independent of e such that (43) | F4(r, r')| + 8V* , m ST r> r or + + -,(r,r') ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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