## Linear Operators: Spectral theory |

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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

and 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 |Jož| < g (**) 2 (Hint: Use Exercise 33and the ...

Page 1275

Jacobi

problem made in Section 8 can be carried considerably farther ... An infinite

—q| > 1.

Jacobi

**Matrices**and the Moment Problem The investigations of the momentproblem made in Section 8 can be carried considerably farther ... An infinite

**matrix**{ak}, j, k > 0, is said to be a Jacobi**matrix**if (i) (l pa (ii) ('pa day. all p, q, 0, p—q| > 1.

Page 1361

It follows from the spectral theorem that there exist

Ao) = UAUT", where U = {uv} is a unitary

where A1, ..., A, are the eigenvalues of S(Ao) each repeated according to its ...

It follows from the spectral theorem that there exist

**matrices**U and A such that S(Ao) = UAUT", where U = {uv} is a unitary

**matrix**and A is the**matrix**{ai}} = {2,3,4},where A1, ..., A, are the eigenvalues of S(Ao) each repeated according to its ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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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