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

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Page 955

The letter cl will

be the isometric isomorphism of 21 onto C(.,l) whose existence is asserted by

Corollary IX.8.8. For f in L1(R), we usually write -r(Tf) simply as -rf. The letter E will

...

The letter cl will

**denote**the space of maximal ideals of QI, and 1': QI -> C(.I) willbe the isometric isomorphism of 21 onto C(.,l) whose existence is asserted by

Corollary IX.8.8. For f in L1(R), we usually write -r(Tf) simply as -rf. The letter E will

...

Page 1126

of the closed set C; we shall

. Since each projection in the spectral resolution of T and hence each continuous

function of T is a strong limit of linear combinations of the projections Ei, ...

of the closed set C; we shall

**denote**this subspace of L2[0, 1] by the symbol L2(C). Since each projection in the spectral resolution of T and hence each continuous

function of T is a strong limit of linear combinations of the projections Ei, ...

Page 1486

In the next few paragraphs r

operator of order n, defined on the interval R = {— 00 < t < + co}. Let -r have the

form oi and suppose that all the coefficients al are periodic and have the same

period.

In the next few paragraphs r

**denotes**a formally self adjoint formal differentialoperator of order n, defined on the interval R = {— 00 < t < + co}. Let -r have the

form oi and suppose that all the coefficients al are periodic and have the same

period.

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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