## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1290

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. 10 ( 1 ) that since the ( 127 ) * , the operator d d P. dt dt n is

way ...

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. 10 ( 1 ) that since the ( 127 ) * , the operator d d P. dt dt n is

**formally self adjoint**provided only that the coefficients pi are real . In the sameway ...

Page 1295

If the ( regular or irregular ) formal differential operator r is

then the operator T. ( T ) is symmetric . PROOF . Clearly To ( t ) C T ( T ) .

Corollary 5 shows that Ti ( 7 ) C T. ( ) * . Q.E.D. We recall ( cf. Definition XII.4.9 )

that if t is ...

If the ( regular or irregular ) formal differential operator r is

**formally self adjoint**then the operator T. ( T ) is symmetric . PROOF . Clearly To ( t ) C T ( T ) .

Corollary 5 shows that Ti ( 7 ) C T. ( ) * . Q.E.D. We recall ( cf. Definition XII.4.9 )

that if t is ...

Page 1400

Let T be a

with at least one fixed end point . Let 2 be an arbitrary real point not belonging to

the essential spectrum of t . Then the deficiency indices of t are both equal to an ...

Let T be a

**formally self adjoint**formal differential operator defined on an interval Iwith at least one fixed end point . Let 2 be an arbitrary real point not belonging to

the essential spectrum of t . Then the deficiency indices of t are both equal to an ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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### Common terms and phrases

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 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