## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1272

If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency

If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency

**indices**are different from zero . A maximal symmetric operator is one which has no proper symmetric extensions ...Page 1398

Let T be a formally self adjoint formal differential operator defined on an interval I. If the minimum of the deficiency

Let T be a formally self adjoint formal differential operator defined on an interval I. If the minimum of the deficiency

**indices**of T ( T ) is k , then for 1 0 0 ( t ) the equation to = lo has at least k linearly independent solutions ...Page 1611

( 1 ) If the essential spectrum of r is not the entire real axis , the deficiency

( 1 ) If the essential spectrum of r is not the entire real axis , the deficiency

**indices**of 1 are equal ( 6.6 ) . ( 2 ) In particular , the deficiency**indices**are equal if t is bounded below . ( 3 ) If for some real or complex 2 all ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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 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 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