## Linear Operators, Part 2 |

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Results 1-3 of 52

Page 1332

Hence, by the remark following Corollary 1.5, the range of E(}.) is at most n-

dimensional. This proves (b). To prove (c), we have only to show that the set of

have ...

Hence, by the remark following Corollary 1.5, the range of E(}.) is at most n-

dimensional. This proves (b). To prove (c), we have only to show that the set of

**eigenfunctions**of T is complete. Since for each element f of our Hilbert space wehave ...

Page 1383

Again we are in the situation of Section 4, the interval being finite, the spectrum

being discrete, and the set of

conditions A and C, the unique solution of 130 = 1.0 satisfying the boundary

condition ...

Again we are in the situation of Section 4, the interval being finite, the spectrum

being discrete, and the set of

**eigenfunctions**being complete. With boundaryconditions A and C, the unique solution of 130 = 1.0 satisfying the boundary

condition ...

Page 1617

The main results of these papers are the following: (1) Haar [3] proved that for the

Sturm-Liouville

boundary conditions (a) there exist continuous functions whose Sturm-Liouville

series is ...

The main results of these papers are the following: (1) Haar [3] proved that for the

Sturm-Liouville

**eigenfunctions**obtained by the impositions of separatedboundary conditions (a) there exist continuous functions whose Sturm-Liouville

series is ...

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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