## Linear Operators: Spectral theory |

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Page 985

A set of functions on R is said to be

A set of functions on R is said to be

**closed**under translations if , for every y in R , t , belongs to the set whenever | does . 6 LEMMA . The**closed**linear manifold determined by the translates of the functions in a set S ĒL ( R ) ...Page 1245

The Canonical Factorization In this section we shall prove that each

The Canonical Factorization In this section we shall prove that each

**closed**operator T with dense domain in Hilbert space has a unique factorization T PA , where A is a positive ( i.e. , ( Ax , x ) 2 0 , x € D ( A ) ) self adjoint ...Page 1283

Thus Theorem 1 is proved for the special case in which I is a

Thus Theorem 1 is proved for the special case in which I is a

**closed**interval . Now suppose that I is not known to be**closed**. It still follows from the proof given above that if J is any**closed**subinterval of I containing the point to ...### 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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