## Linear Operators, Part 2 |

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Page 978

nondiscrete locally compact Abelian group and integration will always be

performed with respect to a Haar measure on the group. It was observed in

Corollary 5.2 that ...

**Closure**Theorems As in the preceding section the letter R will stand for anondiscrete locally compact Abelian group and integration will always be

performed with respect to a Haar measure on the group. It was observed in

Corollary 5.2 that ...

Page 1226

7 DEFINITION. The minimal closed symmetric extension of a symmetric operator

T with dense domain is called its

* ).

7 DEFINITION. The minimal closed symmetric extension of a symmetric operator

T with dense domain is called its

**closure**, and written T. 8 LEMMA. (a) The**closure**T of T is the restriction of T* to the**closure**of 'D(T) in the Hilbert space 'D(T* ).

Page 1686

-V 5 THEOREM. Let n g 1, and let D be a bounded open set in Euclidean space E

". Suppose that the boundary 0/ D is a smooth sur/ace and that no point in the

boundary of D is interior to the

...

-V 5 THEOREM. Let n g 1, and let D be a bounded open set in Euclidean space E

". Suppose that the boundary 0/ D is a smooth sur/ace and that no point in the

boundary of D is interior to the

**closure**of D. Letkgl andmg0beintegers. Let oogpgl...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero