## Linear Operators: Spectral theory |

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Page 1332

To prove (c), we have only to show that the set of

... have a compact resolvent, it is worth pausing for a moment to give an

elementary but useful result on the pointwise convergence of

expansions.

To prove (c), we have only to show that the set of

**eigenfunctions**of T is complete.... have a compact resolvent, it is worth pausing for a moment to give an

elementary but useful result on the pointwise convergence of

**eigenfunction**expansions.

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 r3a = Act 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 r3a = Act satisfying the boundary

condition ...

Page 1617

in the study of convergence in Lp. The main results of these papers are the

following: (1) Haar [3] proved that for the Sturm-Liouville

obtained by the impositions of separated boundary conditions (a) there exist

continuous ...

in the study of convergence in Lp. The main results of these papers are the

following: (1) Haar [3] proved that for the Sturm-Liouville

**eigen- functions**obtained by the impositions of separated boundary conditions (a) there exist

continuous ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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