## Linear Operators: Spectral theory |

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Page 1590

The work of Hilbert [1] in 1904 already contains a remark to the effect that Green's

kernel for an operator of the

Hilbert-Schmidt type. As soon as the results of Hilbert and E. Schmidt on such ...

The work of Hilbert [1] in 1904 already contains a remark to the effect that Green's

kernel for an operator of the

**second order**on a compact interval is a kernel of theHilbert-Schmidt type. As soon as the results of Hilbert and E. Schmidt on such ...

Page 1834

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

detection of the oscillation of a

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

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. DukeMath. J. 17, 57–62 (1950). 4. On self-adjoint differential equations of

**second****order**.Page 1848

Spectral functions of a symmetric operator. Izvestiya Akad. Nauk SSSR (N. S.) 4,

277–318 (1940). (Russian. English summary) Math. Rev. 2, 105 (1941). 9. On the

spectrum of singular non-self-adjoint differential operators of the

Spectral functions of a symmetric operator. Izvestiya Akad. Nauk SSSR (N. S.) 4,

277–318 (1940). (Russian. English summary) Math. Rev. 2, 105 (1941). 9. On the

spectrum of singular non-self-adjoint differential operators of the

**second order**.### What people are saying - Write a review

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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