## Linear Operators: Spectral theory |

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Page 1239

Conversely , let T , be a self adjoint

restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of

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

Conversely , let T , be a self adjoint

**extension**of T. Then by Lemma 26 , T , is therestriction of T * to a subspace W of D ( T * ) determined by a symmetric family of

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

Page 1270

symmetric operator has a self adjoint

determining whether the spectral theorem may be employed . If the answer to this

...

**Extensions**of symmetric operators . The problem of determining whether a givensymmetric operator has a self adjoint

**extension**is of crucial importance indetermining whether the spectral theorem may be employed . If the answer to this

...

Page 1395

Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points

of the spectrum of a self adjoint

particular

...

Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points

of the spectrum of a self adjoint

**extension**T of To ( t ) is independent of theparticular

**extension**chosen , i.e. , is independent of the particular set of boundary...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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 complete 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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk 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