## 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

In that

on the basis of this theory, will discuss a ... Qualitative Theory of the Deficiency

Index The methods developed in

In that

**section**we shall first develop a part of the theory of “special functions,” andon the basis of this theory, will discuss a ... Qualitative Theory of the Deficiency

Index The methods developed in

**Section**5, especially the TitchmarshKodaira ...Page 1590

that Green's kernel for an operator of the second order on a compact interval is a

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

**Section**4. The work of Hilbert [1] in 1904 already contains a remark to the effectthat Green's kernel for an operator of the second order on a compact interval is a

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

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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