## Linear Operators, Part 2 |

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Page 950

(G) for E in Z', where F varies over the closed subsets of E and G over the open

sets containing E. Such a measure is unique up to multiplication by positive

numbers, and is called

(G) for E in Z', where F varies over the closed subsets of E and G over the open

sets containing E. Such a measure is unique up to multiplication by positive

numbers, and is called

**Haar measure**. In the case R = (—oO, + 00), the**Haar****measure**...Page 1152

The existence of an invariant

countability was first shown by

discussed by von Neumann [17]. Other proofs of existence or uniqueness have ...

The existence of an invariant

**measure**on a group satisfying the second axiom ofcountability was first shown by

**Haar**[1], and the question of uniqueness was firstdiscussed by von Neumann [17]. Other proofs of existence or uniqueness have ...

Page 1154

0-compact group R and let 1. be a H aar measure in R. Then the product

measure A >< 1 is a

= R X R is locally compact and 0-compact, it has a

its ...

0-compact group R and let 1. be a H aar measure in R. Then the product

measure A >< 1 is a

**Haar measure**in R >< R. Pnoor. Since the product group Rm= R X R is locally compact and 0-compact, it has a

**Haar measure**1(2) defined onits ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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