## Linear Operators: Spectral theory |

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Page 1787

Math. Soc. 61, 122–127 (1947). - 4. Spectral resolution of groups of unitary

operators.

compactifications of a locally compact abelian group, I, II. I. Proc. Imp. Acad.

Tokyo 19 ...

Math. Soc. 61, 122–127 (1947). - 4. Spectral resolution of groups of unitary

operators.

**Duke Math**. J. 11, 589–595 (1944). Anzai, H., and Kakutani, S. 1. Bohrcompactifications of a locally compact abelian group, I, II. I. Proc. Imp. Acad.

Tokyo 19 ...

Page 1827

York, 1955. 6. Commutative operator algebras. Proc. Nat. Acad. Sci. U.S.A. 38,

598–605 (1952). Kelley, J. L., and Vaught, R. L. 1. The positive come in Banach ...

**Duke**.**Math**. J. 17,. 277–283. (1950). General topology. D. van Nostrand, NewYork, 1955. 6. Commutative operator algebras. Proc. Nat. Acad. Sci. U.S.A. 38,

598–605 (1952). Kelley, J. L., and Vaught, R. L. 1. The positive come in Banach ...

Page 1834

second order. J. London Math. Soc. ... Math. 9, 37–44 (1927). Lengyel, B. A. 1. On

the spectral theorem of self-adjoint operators. Acta Sci. Math. Szeged 9, 174–186

...

**Duke Math**. J. 17, 57–62 (1950). 4. On self-adjoint differential equations ofsecond order. J. London Math. Soc. ... Math. 9, 37–44 (1927). Lengyel, B. A. 1. On

the spectral theorem of self-adjoint operators. Acta Sci. Math. Szeged 9, 174–186

...

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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