## Linear operators: Spectral operators |

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Page 1926

n = 0 -le<j(T) W! If T is a normal operator, then (21 — XI)E(X) = 0 and this formula

reduces to the formula f(T)= £ f(X)E(X), Aeo(T) which is not valid for an

To see more clearly the difference between the calculi given by these two ...

n = 0 -le<j(T) W! If T is a normal operator, then (21 — XI)E(X) = 0 and this formula

reduces to the formula f(T)= £ f(X)E(X), Aeo(T) which is not valid for an

**arbitrary**T.To see more clearly the difference between the calculi given by these two ...

Page 2031

To prove (iv) suppose first that tp is in <t> in which case a permissible

interchange of integration gives (FT*)(<p) = f (F<p)(sW(s) ds = f <p(s)(F<l,)(s) ds =

TF,(«p), <p e <Z>. JRN JrN Now 0 is dense in § = L2(RN) and thus there is for an

To prove (iv) suppose first that tp is in <t> in which case a permissible

interchange of integration gives (FT*)(<p) = f (F<p)(sW(s) ds = f <p(s)(F<l,)(s) ds =

TF,(«p), <p e <Z>. JRN JrN Now 0 is dense in § = L2(RN) and thus there is for an

**arbitrary**...Page 2314

Let k0 , fcj be

defined by the formal differential operator t = —(djdt)2 and the boundary

conditions /(0)-*0/'(0)=0, /(l)-t1/'(l)=0. Then T is a spectral operator satisfying all

the ...

Let k0 , fcj be

**arbitrary**constants and let T be the unbounded operator in L2(0, 1)defined by the formal differential operator t = —(djdt)2 and the boundary

conditions /(0)-*0/'(0)=0, /(l)-t1/'(l)=0. Then T is a spectral operator satisfying all

the ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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