## Linear Operators: Spectral theory |

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Page 1164

Calderón and Zygmund [1] show that if the function Q

weak, continuity hypothesis, then the singular integral (i) exists for almost all w if f

is in L1(E") or L,(E"), co-p-1, (cf. Exercise 8.23); (ii)

Calderón and Zygmund [1] show that if the function Q

**satisfies**a suitable, ratherweak, continuity hypothesis, then the singular integral (i) exists for almost all w if f

is in L1(E") or L,(E"), co-p-1, (cf. Exercise 8.23); (ii)

**satisfies**salq (r)"To da ~ 0 if ...Page 1316

5 LEMMA. The function K(c, .) obtained from the kernel defined in the preceding

lemma by firing c in I,

defining To. PRoof. The notation of the proof of the preceding lemma will be used

.

5 LEMMA. The function K(c, .) obtained from the kernel defined in the preceding

lemma by firing c in I,

**satisfies**the boundary conditions Bo (f) = 0, i = 1,..., k",defining To. PRoof. The notation of the proof of the preceding lemma will be used

.

Page 1602

(48) Suppose that the function q is bounded below, and let f be a real solution of

the equation (2–1)f = 0 on [0, oo) which is not square-integrable but which

spectrum ...

(48) Suppose that the function q is bounded below, and let f be a real solution of

the equation (2–1)f = 0 on [0, oo) which is not square-integrable but which

**satisfies**|f(s) as – ot) for some k > 0. Then the point à belongs to the essentialspectrum ...

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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