## Linear Operators, Part 2 |

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Page 1333

adjoint operators T derived from formal differential operators in the case where

the resolvent of T is compact was discussed. We turn in this section to the study ...

**Spectral Theory**: General Case In the preceding section the**spectral theory**of selfadjoint operators T derived from formal differential operators in the case where

the resolvent of T is compact was discussed. We turn in this section to the study ...

Page 1803

Ann. of Math. (2) 41, 689-661 (1940).

687-651 (1948).

Math. Soc. 54, 185-217 (1948). Integration and linear operations. Trans. Amer.

Math.

Ann. of Math. (2) 41, 689-661 (1940).

**Spectral theory**. Bull. Amer. Math. Soc. 49,687-651 (1948).

**Spectral theory**1, ('onvergence to projections. Trans. Amer.Math. Soc. 54, 185-217 (1948). Integration and linear operations. Trans. Amer.

Math.

Page 1804

reduction problem in

Cambridge, Mass., 1950, Vol. 2, 115-122.

identity.

**Spectral theory**. Proc. Symposium on**Spectral Theory**etc., 203-208 (1951). Thereduction problem in

**spectral theory**. Proc. International Congress Math.,Cambridge, Mass., 1950, Vol. 2, 115-122.

**Spectral theory**. II. Resolutions of theidentity.

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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