## Linear Operators: Spectral theory |

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Page 853

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

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 856

Adjoints and Boundary Values of Differential Operators . . Resolvents of

Differential Operators . .

General Case . . . . Qualitative Theory of the Deficiency Index . . Qualitative

Theory of the ...

Adjoints and Boundary Values of Differential Operators . . Resolvents of

Differential Operators . .

**Spectral Theory**: Compact Resolvents . .**Spectral Theory**:General Case . . . . Qualitative Theory of the Deficiency Index . . Qualitative

Theory of the ...

Page 1333

adjoint operators T derived from formal differential operators in the case where

the resolvent of T is compact was discussed. We turn in this section to the study ...

**Spectral Theory**: General Case In the preceding section the**spectral theory**of selfadjoint operators T derived from formal differential operators in the case where

the resolvent of T is compact was discussed. We turn in this section to the study ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

17 other sections not shown

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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