## Linear Operators: Spectral theory |

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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

The minimal closed symmetric extension of a symmetric operator T with dense

domain is called its

restriction of To to the

T ...

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 therestriction of To to the

**closure**of Q(T) in the Hilbert space 3 (T"). (b) The operatorT ...

Page 1686

5 THEOREM. Let n > 1, and let D be a bounded open set in Euclidean space E”.

Suppose that the boundary of D is a smooth surface and that no point in the

boundary of D is interior to the

OO ...

5 THEOREM. Let n > 1, and let D be a bounded open set in Euclidean space E”.

Suppose that the boundary of D is a smooth surface and that no point in the

boundary of D is interior to the

**closure**of D. Let k > 1 and m > 0 be integers. LetOO ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero