## Linear Operators: Spectral theory |

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Results 1-3 of 81

Page 1164

Singular integrals and inequalities. The general inequalities of Section 7 are due

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

Singular integrals and inequalities. The general inequalities of Section 7 are due

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 ...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 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### 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 Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 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