## Linear Operators, Volume 2 |

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Page 1226

Part ( a ) follows immediately from

Part ( a ) follows immediately from

**Lemma**5 ( b ) , and part ( b ) follows immediately from part ( a ) and**Lemma**5 ( c ) . Q.E.D. It follows from**Lemma**6 ( b ) that any symmetric operator with dense domain has a unique minimal closed ...Page 1696

By

By

**Lemma**14 there is a sequence { Fm } of elements of D ( I ) , each of which has a carrier which is a compact subset Cm of ... it follows from**Lemmas**13 , 3.43 and 3.12 that there is a unique extension G of F to a distribution in D ( D ) ...Page 1733

Q.E.D.

Q.E.D.

**Lemma**18 enables us to use the method of proof of Theorem 2 in the neighborhood of the boundary of a domain with ... 19**LEMMA**. Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain 1 ...### 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