## Linear Operators: Spectral operators |

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Page 2068

It is clear that the linear space LQ = L^rs Lm

n C of all inte- grable functions which coincide almost everywhere with a

continuous function clearly

= jLx ...

It is clear that the linear space LQ = L^rs Lm

**satisfies**(11). Also the space L0 = Lxn C of all inte- grable functions which coincide almost everywhere with a

continuous function clearly

**satisfies**(11). Example 11.12 shows that the space L0= jLx ...

Page 2112

An example is given to show that not every operator admits a duality theory of

type 1; however, if T

interior of Fa , then T does admit such a duality theory. It is a distinctly non-trivial

fact ...

An example is given to show that not every operator admits a duality theory of

type 1; however, if T

**satisfies**the condition: (a) 9l(Flt T) g Wl(F a , T), if Ft e theinterior of Fa , then T does admit such a duality theory. It is a distinctly non-trivial

fact ...

Page 2399

Then the equation to = 0 has two solutions a1 and a2 satisfying the asymptotic

relationships aj(<) ~ 1, a2(t) ~ t as t-> oo. Proof. We saw in Corollary 2 that a^t) =

a^t, 0)

t) ...

Then the equation to = 0 has two solutions a1 and a2 satisfying the asymptotic

relationships aj(<) ~ 1, a2(t) ~ t as t-> oo. Proof. We saw in Corollary 2 that a^t) =

a^t, 0)

**satisfies**the first of these asymptotic relationships. Let a be so large that a^t) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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