## Linear operators: Spectral operators |

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Page 1978

Since E(o; A) is bounded in a, \E(o;A)Ek&\-£\E(o;A)\-gK, oe£, for some

The restriction A \ Ek9)p satisfies the condition (i) on the set Sfc, and so it follows

from what has already been proved that E(o; A) | Ek §p = I" E(a; A(a))e(ds) \ Ek ...

Since E(o; A) is bounded in a, \E(o;A)Ek&\-£\E(o;A)\-gK, oe£, for some

**constant**K.The restriction A \ Ek9)p satisfies the condition (i) on the set Sfc, and so it follows

from what has already been proved that E(o; A) | Ek §p = I" E(a; A(a))e(ds) \ Ek ...

Page 2439

Let us now note that there exists a positive absolute

— aco'|^c|ct) — a>'\ for all 0 < a < 1 and all w, oo' e E. Indeed, if 6 is the angle

between oo and oo', it is clear that \oo — aco'| > 1 if tt/2 ^ |0| ^ tt, while (32) \w ...

Let us now note that there exists a positive absolute

**constant**c such that (31) \co— aco'|^c|ct) — a>'\ for all 0 < a < 1 and all w, oo' e E. Indeed, if 6 is the angle

between oo and oo', it is clear that \oo — aco'| > 1 if tt/2 ^ |0| ^ tt, while (32) \w ...

Page 2441

... x>) as a -»□ oo. This shows that there exists a finite absolute

that 7(a)| ^ c'(l + |a|)-n + 1. Using this inequahty and using (37), we see that there

exists a finite

... x>) as a -»□ oo. This shows that there exists a finite absolute

**constant**c' suchthat 7(a)| ^ c'(l + |a|)-n + 1. Using this inequahty and using (37), we see that there

exists a finite

**constant**M" independent of e such that (43) \Vi{r,r')\ + BVt dr (r, r') ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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