## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 40

Page 1332

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

Since for each element f of our Hilbert space we have f = X E(2)f, Ae or (T) and

since we have observed above that E(2)f is an

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 we have f = X E(2)f, Ae or (T) and

since we have observed above that E(2)f is an

**eigenfunction**of T, this is obvious.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 tao = Ao 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 tao = Ao satisfying the boundary

condition ...

Page 1617

in the study of convergence in L, The main results of these papers are the

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

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

in the study of convergence in L, The main results of these papers are the

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

**eigenfunctions**obtainedby the impositions of separated boundary conditions (a) there exist continuous ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

17 other sections not shown

### Other editions - View all

### 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