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

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Page 1239

Conversely , let T , be a self

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

Extensions of symmetric operators . The problem of determining whether a given

symmetric operator has a self

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

...

Extensions of symmetric operators . The problem of determining whether a given

symmetric operator has a self

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

...

Page 1400

Then the deficiency indices of t are both equal to an integer k and ( a ) for every

self

at most k ; ( b ) there exist self

Then the deficiency indices of t are both equal to an integer k and ( a ) for every

self

**adjoint extension**T of T ( T ) , the dimension of the null - space { f \ T / = 2f } isat most k ; ( b ) there exist self

**adjoint extensions**T of T. ( T ) such that 2 € 0 ( T ) ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

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 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