## Linear Operators: Spectral theory |

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Page 1223

In the theory of bounded operators, we have only to verify

T is everywhere defined and

situation is quite different. Consider, as an example, an operator which will be ...

In the theory of bounded operators, we have only to verify

**symmetry**(T* QT), for ifT is everywhere defined and

**symmetric**, then To = T. But if T is unbounded thesituation is quite different. Consider, as an example, an operator which will be ...

Page 1236

A set of boundary conditions B, (a) = 0, i = 1,..., k, is said to be

equations B, (a) = B,(y) = 0, i = 1,..., k, imply the equation {a, y} = 0. 26 LEMMA.

Let T be an operator with finite deficiency indices. Every closed

eatension ...

A set of boundary conditions B, (a) = 0, i = 1,..., k, is said to be

**symmetric**if theequations B, (a) = B,(y) = 0, i = 1,..., k, imply the equation {a, y} = 0. 26 LEMMA.

Let T be an operator with finite deficiency indices. Every closed

**symmetric**eatension ...

Page 1272

Marimal

then it has proper

are different from zero. A marimal

...

Marimal

**symmetric**operators. If T is a**symmetric**operator with dense domain,then it has proper

**symmetric**extensions provided both of its deficiency indicesare different from zero. A marimal

**symmetric**operator is one which has no proper...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity 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