## Linear Operators: Spectral theory |

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Results 1-3 of 84

Page 1550

Bellman) Suppose that every solution of the equation t/ = 0 is of class Lp(I) and

that every solution of the equation t*/ = 0 is of class LV(I) (p-1+?_1 = 1).

...

**Prove**that the essential spectrum of the operator t in LV(I) is the empty set. E8 (Bellman) Suppose that every solution of the equation t/ = 0 is of class Lp(I) and

that every solution of the equation t*/ = 0 is of class LV(I) (p-1+?_1 = 1).

**Prove**that...

Page 1557

Suppose that q is bounded below, and suppose that X does not belong to the

essential spectrum of r. Let / be a square-integrable solution of the equation {X—t

)f — 0, ...

**Prove**that the point X belongs to the essential spectrum of z. G20 (Wintner).Suppose that q is bounded below, and suppose that X does not belong to the

essential spectrum of r. Let / be a square-integrable solution of the equation {X—t

)f — 0, ...

Page 1560

G30 Suppose that N(t) = 0(fi log t), and

values at infinity. G81

d): if J' max ( -q(s), 0)ds = 0(t* log2 t), then the operator t has no boundary ...

G30 Suppose that N(t) = 0(fi log t), and

**prove**that the operator r has no boundaryvalues at infinity. G81

**Prove**the following refinement of the result of Exercise Gl9(d): if J' max ( -q(s), 0)ds = 0(t* log2 t), then the operator t has no boundary ...

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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