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

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Page 1420

If A is considered as a subset of H , then the restriction of T ( 7 ' ) to A is a continuous mapping of A into H. Then , assuming that t + t ' has a non -

If A is considered as a subset of H , then the restriction of T ( 7 ' ) to A is a continuous mapping of A into H. Then , assuming that t + t ' has a non -

**zero**leading coefficient , ( A ) the Hilbert spaces D ( T2 ( t + t ' ) ) and D ...Page 1432

Suppose first that the end point under consideration is finite so that without loss of generality we can suppose it to be at

Suppose first that the end point under consideration is finite so that without loss of generality we can suppose it to be at

**zero**. Then , dividing through if necessary by the leading coefficient a , of 1 , we can write the equation ( T ...Page 1727

... In + 1 , ... , In ] and L = [ li , ... , in ] By ( 1 ) and by the definitions ( 2 ) , ( 3 ) , and ( 5 ) of Sı , it follows that ( 7 ) ( SL9 ) ( x ) = 0,9EC ( E " ) , -k Smin ( L ) < max ( L ) 3 k , if one of X1 , ... , xn is

... In + 1 , ... , In ] and L = [ li , ... , in ] By ( 1 ) and by the definitions ( 2 ) , ( 3 ) , and ( 5 ) of Sı , it follows that ( 7 ) ( SL9 ) ( x ) = 0,9EC ( E " ) , -k Smin ( L ) < max ( L ) 3 k , if one of X1 , ... , xn is

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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