## Linear Operators, Part 2 |

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Page 1803

1 2 8 4 5 7 On some

application to generalisation of a theorem of Lebesgue. Mat. Sbornik N. S. 20 (62

), 817-829 (1947). (Russian, English summary) Math. Rev. 9, 19 (1948). On the

basis ...

1 2 8 4 5 7 On some

**properties**of completely additive set functions and theirapplication to generalisation of a theorem of Lebesgue. Mat. Sbornik N. S. 20 (62

), 817-829 (1947). (Russian, English summary) Math. Rev. 9, 19 (1948). On the

basis ...

Page 1900

Almost periodic functions, definition, lV.2.25 (242) space of, additional

1V.15 (ave) definition, lV.2.25 (242) remarks concerning, (386-387) study of, IV.7

Almost uniform (or )4-uniform convergence) definition, 111. 6.1(145). (See also ...

Almost periodic functions, definition, lV.2.25 (242) space of, additional

**properties**,1V.15 (ave) definition, lV.2.25 (242) remarks concerning, (386-387) study of, IV.7

Almost uniform (or )4-uniform convergence) definition, 111. 6.1(145). (See also ...

Page 1902

Category theorem, of Baire, 1.6.9 (20) Cauchy integral formula, (227) for

functions of an operator, in a finite dimensional space, V11.1.10 (560) in general

space, VII.8.9 ...

**properties**, 1.3.12-14 (9) Cartesian product of topological spaces, 1.8 (81)Category theorem, of Baire, 1.6.9 (20) Cauchy integral formula, (227) for

functions of an operator, in a finite dimensional space, V11.1.10 (560) in general

space, VII.8.9 ...

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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