## 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 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero