## Linear Operators: Spectral theory |

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Page 1787

Studia Math. 13, 194–207 (1953). 4. Mean ergodic theorem in locally conver

linear topological spaces. Studia Math. ... Math. Soc. 61, 122–127 (1947). - 4.

Spectral resolution of groups of unitary operators.

1944).

Studia Math. 13, 194–207 (1953). 4. Mean ergodic theorem in locally conver

linear topological spaces. Studia Math. ... Math. Soc. 61, 122–127 (1947). - 4.

Spectral resolution of groups of unitary operators.

**Duke Math**. J. 11, 589–595 (1944).

Page 1827

Trans. Amer.

implies the ariom of choice. Fund.

1955. 6.

Trans. Amer.

**Math**. Soc. 72, 323–326 (1952). 3. The Tychonoff product theoremimplies the ariom of choice. Fund.

**Math**. ... Convergence. in. topology.**Duke**.**Math**. J. 17,. 277–283. (1950). General topology. D. van Nostrand, New York,1955. 6.

Page 1834

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 3. On the

detection of the oscillation of a second order linear differential equation.

order.

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 3. On the

detection of the oscillation of a second order linear differential equation.

**Duke****Math**. J. 17, 57–62 (1950). 4. On self-adjoint differential equations of secondorder.

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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