## Linear Operators: Spectral theory |

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Page 1218

... is a Borel set o in R with ulo ) < ε and such that the

complement of o is continuous . Proof . If the

then so is the

having ...

... is a Borel set o in R with ulo ) < ε and such that the

**restriction**of f to thecomplement of o is continuous . Proof . If the

**restrictions**flo , gd are continuousthen so is the

**restriction**( af + ßglo od and thus the class of measurable functionshaving ...

Page 1239

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

is the

family of linearly independent boundary conditions Bi ( x ) = 0 , i = 1 , . . . , k , and

we ...

_ _ _ 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 symmetricfamily of linearly independent boundary conditions Bi ( x ) = 0 , i = 1 , . . . , k , and

we ...

Page 1471

31 , a set of boundary conditions defining a self adjoint

the form B ( A ) = Q767 ( 1 ) + & , G2 ( 1 ) = 0 , ai taš # 0 , Q1 , Q , real , B ( ) = B ,

G7 ( / ) + B2G2 ( / ) = 0 , $ { + B2 # 0 , B1 , B , real , if ı has boundary values both at

...

31 , a set of boundary conditions defining a self adjoint

**restriction**T of Ti ( t ) is ofthe form B ( A ) = Q767 ( 1 ) + & , G2 ( 1 ) = 0 , ai taš # 0 , Q1 , Q , real , B ( ) = B ,

G7 ( / ) + B2G2 ( / ) = 0 , $ { + B2 # 0 , B1 , B , real , if ı has boundary values both at

...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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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 consider 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 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