## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1211

Under

the Cartesian product of S and the real number system R which is measurable

with respect to the product of v and the measure /4 = (E(-)g, g), and which has the

...

Under

**Hypothesis**7, there is, for each g in L2(S, Z', v), a function W defined onthe Cartesian product of S and the real number system R which is measurable

with respect to the product of v and the measure /4 = (E(-)g, g), and which has the

...

Page 1215

Hence the expansion f = Leata determined by the direct sum decomposition H =

EV , takes the form stated in the following corollary . 12 COROLLARY . With the

notation and

Hence the expansion f = Leata determined by the direct sum decomposition H =

EV , takes the form stated in the following corollary . 12 COROLLARY . With the

notation and

**hypothesis**of the preceding theorem we have f ( s ) = 2 / ( Una ( a ) ...Page 1733

Since , by the inductive

of Hymy - ( C ) onto H. ( C ) HP ) ( C ) , it follows that 11 - ' 10S - 1 ) | ık ) is

uniformly bounded in 1 , from which the present lemma follows , as has been

shown ...

Since , by the inductive

**hypothesis**, ( o + K ) -1 is a uniformly bounded mappingof Hymy - ( C ) onto H. ( C ) HP ) ( C ) , it follows that 11 - ' 10S - 1 ) | ık ) is

uniformly bounded in 1 , from which the present lemma follows , as has been

shown ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix measure multiplicity Nauk 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