## Linear Operators: Spectral theory |

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Page 1176

Let p, q, k, be as in the preceding lemma, and, for each N, let of w be the

transformation in L,(l,) which maps the

Fourier transform f($) into the

transform k,($)f,($) ...

Let p, q, k, be as in the preceding lemma, and, for each N, let of w be the

transformation in L,(l,) which maps the

**vector**whose nth component has theFourier transform f($) into the

**vector**whose nth component has the Fouriertransform k,($)f,($) ...

Page 1749

V(0, ć1, a2, ara) = Vo(a1, a2, ara), where V = [V1, V., Val is a complex three-

dimensional

i times the magnetic

the ...

V(0, ć1, a2, ara) = Vo(a1, a2, ara), where V = [V1, V., Val is a complex three-

dimensional

**vector**equal to the sum of the “electric”**vector**and the imaginary uniti times the magnetic

**vector**, and where the matrices A1, A2, and As are given bythe ...

Page 1849

Compact metric Boolean algebras and

A. 11, 125–128 (1942). 2. On Fréchet lattices, I. J. Sci. Hirosima Univ. Ser. A. 12,

235–248 (1943). (Japanese) Math. Rev. 10, 544 (1949). 3. Remarks on a

Compact metric Boolean algebras and

**vector**lattices. J. Sci. Hirosima Univ. Ser.A. 11, 125–128 (1942). 2. On Fréchet lattices, I. J. Sci. Hirosima Univ. Ser. A. 12,

235–248 (1943). (Japanese) Math. Rev. 10, 544 (1949). 3. Remarks on a

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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