## Linear Operators: Spectral theory |

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Page 1087

) and L,(S, X, u). Prove that log o (T,) is a convex function of p. 51 Let the

hypotheses of Exercise 50 be satisfied. Show that g(T,) Co.(T,) n g(T,) if pi sp2 s

pa; p1, ...

**Suppose**that for pi, p, in I, T, and T., always agree on the intersection of L.,(S. 2, u) and L,(S, X, u). Prove that log o (T,) is a convex function of p. 51 Let the

hypotheses of Exercise 50 be satisfied. Show that g(T,) Co.(T,) n g(T,) if pi sp2 s

pa; p1, ...

Page 1563

Prove that (4–1)f, = O(V(b.-a,)). (b) Prove that the essential spectrum of r contains

the positive semi-axis. (Hint: Apply Theorem 7.1.) G41

q is bounded below.

Prove that (4–1)f, = O(V(b.-a,)). (b) Prove that the essential spectrum of r contains

the positive semi-axis. (Hint: Apply Theorem 7.1.) G41

**Suppose**that the functionq is bounded below.

**Suppose**that the origin belongs to the essential spectrum ...Page 1602

(47) In [0, oo),

solutions f and g such that |f(s)'ds = o(e) and sig'(s)ods = o(e). Then the point A

belongs to the essential spectrum of r (Hartman and Wintner [14]). (48)

...

(47) In [0, oo),

**suppose**that the equation (2–1)f = 0 has two linearly independentsolutions f and g such that |f(s)'ds = o(e) and sig'(s)ods = o(e). Then the point A

belongs to the essential spectrum of r (Hartman and Wintner [14]). (48)

**Suppose**...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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