## Linear Operators: Spectral operators |

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Page 1080

34 (Bendixon) Let A be as in Exercise 25, and suppose also that the

elements of A are real. Let C = (A – A*), and let g be the maximum of the absolute

values of the

the ...

34 (Bendixon) Let A be as in Exercise 25, and suppose also that the

**matrix**elements of A are real. Let C = (A – A*), and let g be the maximum of the absolute

values of the

**matrix**elements of C. Then |Joã sg (**) 2 (Hint: Use Exercise 33 andthe ...

Page 1275

Jacobi

problem made in Section 8 can be carried considerably farther by applying the

theory of unbounded symmetric operators in Hilbert space to Jacobi

Jacobi

**Matrices**and the Moment Problem The investigations of the momentproblem made in Section 8 can be carried considerably farther by applying the

theory of unbounded symmetric operators in Hilbert space to Jacobi

**matrices**.Page 1361

However, as in the proof of Lemma X.3.3(ii), it is seen that E((20%) # 0 if and only

if Åo is an eigenvalue of T. We shall now show that when the

})} is not zero, one may construct a complete set of orthogonal eigenfunctions ...

However, as in the proof of Lemma X.3.3(ii), it is seen that E((20%) # 0 if and only

if Åo is an eigenvalue of T. We shall now show that when the

**matrix**S(2,) = {p,({A,})} is not zero, one may construct a complete set of orthogonal eigenfunctions ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero