## Linear Operators: Spectral theory |

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Page 1270

The

adjoint extension is of crucial importance in determining whether the spectral

theorem may be employed. If the answer to this

important to ...

The

**problem**of determining whether a given symmetric operator has a selfadjoint extension is of crucial importance in determining whether the spectral

theorem may be employed. If the answer to this

**problem**is affirmative, it isimportant to ...

Page 1622

.1 —-co I. The converse

differential operators to a variety of

shown a physical meaning for many of the mathematical notions, but has also

raised ...

.1 —-co I. The converse

**problem**. The wide application of the spectral theory ofdifferential operators to a variety of

**problems**in modern physics not only hasshown a physical meaning for many of the mathematical notions, but has also

raised ...

Page 1831

Doklady Akad. Nauk SSSR (N. S.) 30, 484–488 (1941). Infinite J-matrices and a

matria moment

Russian) Math. Rev. 11, 670 (1950). On the trace formula in perturbation theory.

Doklady Akad. Nauk SSSR (N. S.) 30, 484–488 (1941). Infinite J-matrices and a

matria moment

**problem**. Doklady Akad. Nauk SSSR (N.S.) 69, 125–128 (1949). (Russian) Math. Rev. 11, 670 (1950). On the trace formula in perturbation theory.

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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