## Linear Operators, Part 2 |

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Page v

While there are some isolated discussions of nonselfadjoint operators, such as

that giving the completeness of the generalized eigenfunctions of Hilbert-Schmidt

operators in

While there are some isolated discussions of nonselfadjoint operators, such as

that giving the completeness of the generalized eigenfunctions of Hilbert-Schmidt

operators in

**Section**XI.6, the general theory of spectral operators and the ...Page 1392

Because of the difficulty of dealing with the various functions which may arise as

solutions of the equation to = 10, we prefer to postpone any further examination

of special eigenfunction expansions to

Because of the difficulty of dealing with the various functions which may arise as

solutions of the equation to = 10, we prefer to postpone any further examination

of special eigenfunction expansions to

**Section**8 below. In that**section**we shall ...Page 1590

For a detailed exposition of the problems connected with the calculation of the

Green's kernel for a differential operator on a finite interval, the recent paper of E.

Mohr [1] may be found valuable.

...

For a detailed exposition of the problems connected with the calculation of the

Green's kernel for a differential operator on a finite interval, the recent paper of E.

Mohr [1] may be found valuable.

**Section**4. The work of Hilbert [1] in 1904 already...

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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