## Linear Operators: Spectral theory |

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Page 1310

shall show the theorem is true in each of the four cases discussed above. In case

(iv), since there are no boundary values, no boundary conditions are imposed; ...

**square**-**integrable**at b and satisfying the boundary conditions at b. PROOF. Weshall show the theorem is true in each of the four cases discussed above. In case

(iv), since there are no boundary values, no boundary conditions are imposed; ...

Page 1556

G16 (Hartman) Suppose that the equation ts = 0 has a solution with a finite

number of zeros. Prove that there exists a solution g of the same equation such

that g(t)-" is

origin.

G16 (Hartman) Suppose that the equation ts = 0 has a solution with a finite

number of zeros. Prove that there exists a solution g of the same equation such

that g(t)-" is

**square**-**integrable**on a semi-axis sufficiently far removed from theorigin.

Page 1557

(A–t)f = 0 has a solution which is not

G20 (Wintner). Suppose that q is bounded below, and suppose that A does not

belong ...

(A–t)f = 0 has a solution which is not

**square**-**integrable**but has a**square**-**integrable**derivative. Prove that the point A belongs to the essential spectrum of t.G20 (Wintner). Suppose that q is bounded below, and suppose that A does not

belong ...

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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