## Linear Operators: Spectral theory |

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Page 1218

... function f on R and every ε > 0 there is a Borel set o in R with M ( o ) < ε and

such that the

... function f on R and every ε > 0 there is a Borel set o in R with M ( o ) < ε and

such that the

**restriction**of f to the complement of o is continuous . PROOF . If the**restrictions**fo , gd are continuous then so is the**restriction**( af + Bg ) lo n d and ...Page 1239

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

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 the

**restriction**of T * to a subspace W of D ( T * ) determined by a symmetric family oflinearly independent boundary conditions B ; ( x ) = 0 , i = 1 , ... , k , and we have ...

Page 1471

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

, B ( t ) = 3,6 ( 1 ) + B , G ( 1 ) = 0 , Bi +82 +0 , B1 , B , real , if has boundary ...

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

**restriction**T of T ( T ) is of the form B ( A ) = QG ( ) + a , G ( / = 0 , a { + až 70, B ( t ) = 3,6 ( 1 ) + B , G ( 1 ) = 0 , Bi +82 +0 , B1 , B , real , if has 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