## Linear Operators, Part 2 |

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Results 1-3 of 61

Page 1087

it) and Ll,l(S, Z, /1). Prove that log ... 53 Let the hypotheses of Exercise 50 be

satisfied, and

Hermitian.

**Suppose**that for pl, pl in I, T,' and Tl,' always agree on the intersection of L,l(S, X,it) and Ll,l(S, Z, /1). Prove that log ... 53 Let the hypotheses of Exercise 50 be

satisfied, and

**suppose**in addition that the number 2 is in I and that T2 isHermitian.

Page 1563

G41

belongs to the essential spectrum of t. (a) Let {fa} be a sequence in €D(T°(r)) such

that |/"I = 1, It/H] ->0, and such that fa vanishes in the interval [0. n). Set g,,(t) = /,_(

¢) ...

G41

**Suppose**that the function q is bounded below.**Suppose**that the originbelongs to the essential spectrum of t. (a) Let {fa} be a sequence in €D(T°(r)) such

that |/"I = 1, It/H] ->0, and such that fa vanishes in the interval [0. n). Set g,,(t) = /,_(

¢) ...

Page 1602

(48)

the equation (}.—-r)f = 0 on [0, oo) which is not square-integrable but which

satisfies [J1/<s>|=d-I = Ow) for some k > 0. Then the point 2. belongs to the

essential ...

(48)

**Suppose**that the function q is bounded below, and let f be a real solution ofthe equation (}.—-r)f = 0 on [0, oo) which is not square-integrable but which

satisfies [J1/<s>|=d-I = Ow) for some k > 0. Then the point 2. belongs to the

essential ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma 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