## Linear Operators: Spectral theory |

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Page 950

the

compact group, its existence and uniqueness was proved in Theorem 1.1. The

reader who is unfamiliar with

under the ...

the

**Haar measure**may be taken to be Lebesgue measure: in the case of acompact group, its existence and uniqueness was proved in Theorem 1.1. The

reader who is unfamiliar with

**Haar measure**may wish to consult the remarksunder the ...

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

o-compact group R and let à be a

2 × 2 is a

locally compact and g-compact, it has a

o-compact group R and let à be a

**Haar measure**in R. Then the product measure2 × 2 is a

**Haar measure**in RX R. PRoof. Since the product group Roo – R × R islocally compact and g-compact, it has a

**Haar measure**A*) defined on its Borel ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

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