## Linear Operators, Part 2 |

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Page 1147

COROLLARy: If G is a compact topological group satisfying the second axiom of

countability, and G is not a finite set, then any

G is countable. A

COROLLARy: If G is a compact topological group satisfying the second axiom of

countability, and G is not a finite set, then any

**complete**set of representations ofG is countable. A

**complete**set of representations of a finite group is finite.Page 1297

XII.1.6) SD(T1('r)) is

2 are the norm off as an element of H "(J ) it follows easily that §D(T1('r)) is also

...

XII.1.6) SD(T1('r)) is

**complete**in the norm |f11. Since the two additional terms in [f|2 are the norm off as an element of H "(J ) it follows easily that §D(T1('r)) is also

**complete**under the norm 1f|,. As I/|, § |f|, it follows from Theorem II.2.5 that the two...

Page 1903

(See B-space)

compactification of, 1V.6.22 (276), Ix.2.10 (012) definition, lV.6.21 (276), 1X.2.15 (

872) ...

(See B-space)

**Complete**orthonormal set, in Hilbert space, 1V.4.8 (250)**Complete**partially ordered space, definition, 1.8.9 (8) Completely regular space,compactification of, 1V.6.22 (276), Ix.2.10 (012) definition, lV.6.21 (276), 1X.2.15 (

872) ...

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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