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

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Page 1297

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract "

see that the discussion leads us to a number of results about deficiency indices .

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract "

**boundary values**” introduced in the last chapter . We shallsee that the discussion leads us to a number of results about deficiency indices .

Page 1307

______'- -_

a and D1, D1 are

functional A defined by the formula A (f) = 12(7) is also a

______'- -_

**boundary values**C1, C1, D1, D, where C1, C, are**boundary values**ata and D1, D1 are

**boundary values**at b ... formation of complex conjugates, so thefunctional A defined by the formula A (f) = 12(7) is also a

**boundary value**for 1.Page 1471

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

Jacob T. Schwartz. Oi , Oly real , , y real , if 1 has no

if t has

...

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

Jacob T. Schwartz. Oi , Oly real , , y real , if 1 has no

**boundary values**at b ; whileif t has

**boundary values**at b , we may find two real**boundary values**D ,, D , for T...

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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