## Linear Operators, Volume 2 |

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Page 1378

If the determining set 01 , ... , 0 of Theorem 23 were known to be part of a basis 01 , ... , 0 , with the properties of Theorem 13 , then the uniqueness of { ij } would follow immediately from the

If the determining set 01 , ... , 0 of Theorem 23 were known to be part of a basis 01 , ... , 0 , with the properties of Theorem 13 , then the uniqueness of { ij } would follow immediately from the

**preceding**theorem .Page 1419

By the

By the

**preceding**lemma , -f ( t ) sti ( t ) in [ Sit1 , Mi + 1 ] . ... To prove the corollary it suffices to make the change of variable t + -t in the**preceding**corollary . Q.E.D. PROOF OF THEOREM 24. If the function q of Theorem 24 is ...Page 1771

Statement ( i ) follows from the

Statement ( i ) follows from the

**preceding**theorem and Theorem 6.23 . Statement ( ii ) follows from statement ( ii ) of the**preceding**theorem , since a function satisfying the hypotheses of the present statement ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 derivatives 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero