## 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 1816

75, 229-240 (1953). 3. The Lt-solutions of linear differential equations of

separable differential equations. Trans. Amer. Math. Soc. 63, 560-580 (1948). 5.

75, 229-240 (1953). 3. The Lt-solutions of linear differential equations of

**second****order**. Duke Math. J. 14, 323-326 (1947). 4. Unrestricted solution fields of almostseparable differential equations. Trans. Amer. Math. Soc. 63, 560-580 (1948). 5.

Page 1834

On the detection of the oscillation cf a

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

On the detection of the oscillation cf a

**second order**linear differential equation.Duke Math. J. 17, 57-62 (1950). 4. On self-adjoint differential equations of

**second****order**. J. London Math. Soc. 27, 33^7 (1952). Leja, F. 1. Sur la notion du groupe ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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