## Linear Operators, Part 2 |

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Page 970

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in Li ( R ) , L2 ( R ) and f is the

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in Li ( R ) , L2 ( R ) and f is the

**limit**in the norm of L2 ( R ) of the generalized sequence { Xef } . Hence , by Theorem 9 , tf is the ...Page 976

It is easily seen that this theorem asserts that if f is in L2 ( R " ) , the

It is easily seen that this theorem asserts that if f is in L2 ( R " ) , the

**limit**+ N + N sta L ** gt , ... , tn ) ( 21 ) -n / 2 lim f ( x1 , ... , xn ) N J - N -N • exp { -itxi + ... + tnxn ) } dx , ... dxn exists in the norm of L ( R ...Page 1124

If En , E are in F and q ( En ) increases to the

If En , E are in F and q ( En ) increases to the

**limit**( E ) , then it follows from what we have already proved that En is an increasing sequence of projections and E , SE . If Em is the strong**limit**of En , then E. SE and Q ( E ) = Q ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero