## Linear Operators: Spectral theory |

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Page 931

Wermer [5] studied the

invariant under T-1 and such that for some a eost, the vectors T'a, n = 0, 1, 2, ...,

are fundamental in Jl. The

multiplication ...

Wermer [5] studied the

**restriction**of an operator T to a subspace J which is notinvariant under T-1 and such that for some a eost, the vectors T'a, n = 0, 1, 2, ...,

are fundamental in Jl. The

**restriction**of T to Åst is then represented asmultiplication ...

Page 1218

If the

sets 6, with X. au(6,) < e 2 and such that the

Thus ...

If the

**restrictions**flo, g|ó are continuous then so is the**restriction**... Clearly the**restriction**of X, to the complement of o-6 is continuous. ... Now for n > 2 there aresets 6, with X. au(6,) < e 2 and such that the

**restriction**of f, to 6, is continuous.Thus ...

Page 1239

Conversely, let T be a self adjoint extension of T. Then by Lemma 26, T, is the

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Conversely, let T be a self adjoint extension of T. Then by Lemma 26, T, is the

**restriction**of To to a subspace Q3 of Q(T*) determined by a symmetric family oflinearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

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