## Linear Operators: Spectral theory |

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Page 1196

bounded Borel functions into an algebra of normal operators in Hilbert space and thus the above formula

bounded Borel functions into an algebra of normal operators in Hilbert space and thus the above formula

**defines**an ... the self adjoint operator T and let f be a complex Borel function**defined**E - almost everywhere on the real axis .Page 1548

extensions of S and Ŝ respectively , and let 2 , ( T ) and 2n ( f ) be the numbers

extensions of S and Ŝ respectively , and let 2 , ( T ) and 2n ( f ) be the numbers

**defined**for the self adjoint ... and let T , be a self adjoint operator in Hilbert space Hz .**Define**the operator T in H = H , OH , by setting D ( T ) ...Page 1647

In connection with

In connection with

**Definition**4 , it should be noted that two continuous functions**defined**in I which differ at most on a Lebesgue null set are in fact everywhere identical . Thus , by Lemma 3 , a distribution F corresponds to a unique ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator 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 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