## Linear Operators: Spectral theory |

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Page 911

It is clear that we may regard $5 as the direct sum 3 = X $5, of the Hilbert

$52 (cf. Lemma IV.4.19). Theorem 1 may now be applied to the restriction T. of T

to the

It is clear that we may regard $5 as the direct sum 3 = X $5, of the Hilbert

**spaces**$52 (cf. Lemma IV.4.19). Theorem 1 may now be applied to the restriction T. of T

to the

**space**$3, to yield a regular**positive measure**u, vanishing on the ...Page 1173

Let (S, 2, u) be a

kernel defined in E", homogeneous of order 0, smooth except at a = 0, and whose

surface integral over the surface of the unit sphere is zero. Let L.,(L.) denote the ...

Let (S, 2, u) be a

**positive measure space**. Let Q(x) be a numerically-valuedkernel defined in E", homogeneous of order 0, smooth except at a = 0, and whose

surface integral over the surface of the unit sphere is zero. Let L.,(L.) denote the ...

Page 1210

Let T be a self adjoint operator in the Hilbert space La(S, 2, v) where (S. 2, v) is a

bounded on each set in an increasing sequence of sets of finite measure which

covers ...

Let T be a self adjoint operator in the Hilbert space La(S, 2, v) where (S. 2, v) is a

**positive measure space**. Let every element in sh; 13 (T") be v-essentiallybounded on each set in an increasing sequence of sets of finite measure which

covers ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero