## Linear Operators: Spectral operators |

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and the fraction in the

closed operator As cannot be self adjoint, but it always has a resolution of the

identity for S2(«) = (5?-5l)2 + 4ai3, so that the

and the fraction in the

**inequality**(i) of Theorem 6 is St — S: ... the correspondingclosed operator As cannot be self adjoint, but it always has a resolution of the

identity for S2(«) = (5?-5l)2 + 4ai3, so that the

**inequality**(i) of Theorem 6 holds.Page 2190

Thus for some constant K we have \S(f)\ ^ K \f\ and to prove the final

the present theorem it will suffice to prove that |/|£ ^ • Since both terms in this

in ...

Thus for some constant K we have \S(f)\ ^ K \f\ and to prove the final

**inequality**ofthe present theorem it will suffice to prove that |/|£ ^ • Since both terms in this

**inequality**are continuous functions of /, it will suffice to prove it for every function /in ...

Page 2403

First we shall prove an

elementary in the sense that it relates only to the norms of the integral kernels

involved. We then use this

First we shall prove an

**inequality**for integral operators (Lemma 5 below) which iselementary in the sense that it relates only to the norms of the integral kernels

involved. We then use this

**inequality**to apply Theorem 1 in an illustrative but ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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