## Linear Operators, Part 2 |

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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 1591

A version of Lemma 7 is due to Glazman [1, 2]. A result similar to Lemma 8 can

be found in the joint paper of Krein, Krasnosel'skiI and Milman [1]. Theorem 11

was obtained by Weyl for operators of the

Glazman ...

A version of Lemma 7 is due to Glazman [1, 2]. A result similar to Lemma 8 can

be found in the joint paper of Krein, Krasnosel'skiI and Milman [1]. Theorem 11

was obtained by Weyl for operators of the

**second order**, and extended byGlazman ...

Page 1848

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

14, 478 (1958). Investigation of the spectrum and expansion in eigenfunctions of

...

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

**second****order**. Doklady Akad. Nauk SSSR (N .S. ) 85, 41-44 (1952 ). (Russian) Math. Rev.14, 478 (1958). Investigation of the spectrum and expansion in eigenfunctions of

...

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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