## Linear Operators: Spectral theory |

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Page 915

Hilbert space H and let E

sequence { xn } CH such that H = 2 : 1 H ( x ; ) , where Þ ( x ; ) = sp { f ( T ) xilfe Clo

( T ) ) } , and a decreasing sequence { en } of Borel sets such that ( E ( e ) xn ...

Hilbert space H and let E

**denote**its resolution of the identity . Then there exists asequence { xn } CH such that H = 2 : 1 H ( x ; ) , where Þ ( x ; ) = sp { f ( T ) xilfe Clo

( T ) ) } , and a decreasing sequence { en } of Borel sets such that ( E ( e ) xn ...

Page 1126

of the closed set C ; we shall

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 , it ...

of the closed set C ; we shall

**denote**this subspace of L [ 0 , 1 ] by the symbol L (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 , it ...

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In the next few paragraphs t

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

form m idli 2 a , ( 1 ) ( ) , and suppose that all the coefficients a ; are periodic and

have ...

In the next few paragraphs t

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

form m idli 2 a , ( 1 ) ( ) , and suppose that all the coefficients a ; are periodic and

have ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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