## Linear Operators: Spectral theory |

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Page 1164

... to Calderón and Zygmund [1] and [5]; the particular case n = 1 (Hilbert

transform) to M. Riesz. Calderón and Zygmund [1] show that if the function Q

Q - p(x) = ...

... to Calderón and Zygmund [1] and [5]; the particular case n = 1 (Hilbert

transform) to M. Riesz. Calderón and Zygmund [1] show that if the function Q

**satisfies**a suitable, rather weak, continuity hypothesis, then the singular integralQ - p(x) = ...

Page 1385

The function e-Yo

–7 = 0; i.e., if and only if k is positive and A = –1/k”. Thus, only in case (iv) does To

have a non-void point spectrum, which consists of the single point A = –1/k”, ...

The function e-Yo

**satisfies**the boundary condition f(0)-i-kf'(0) if and only if 1 —k V–7 = 0; i.e., if and only if k is positive and A = –1/k”. Thus, only in case (iv) does To

have a non-void point spectrum, which consists of the single point A = –1/k”, ...

Page 1602

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

the equation (A—t)f = 0 on [0, oo) which is not square-integrable but which

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

the equation (A—t)f = 0 on [0, oo) which is not square-integrable but which

**satisfies**|f(s)'ds = o(e) for some k > 0. Then the point % belongs to the essential ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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