## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1178

It is plain from Plancherel's theorem that .1' is a bounded mapping of the space L,

of scalar-valued functions into the space L,(l2) of square~integrable

maps ...

It is plain from Plancherel's theorem that .1' is a bounded mapping of the space L,

of scalar-valued functions into the space L,(l2) of square~integrable

**vector**-**valued**functions. Corollary 19 and Corollary 17 now imply that, for 1 < P < 2, .1'maps ...

Page 1751

differentiable m-

(C,) will denote the subspaces of C°°(C,) consisting of all functions which are

multiply periodic of period 27: and of all functions which vanish outside a

compact ...

differentiable m-

**vector valued**functions defined in C1. Similarly, C:°(C1) and C§°(C,) will denote the subspaces of C°°(C,) consisting of all functions which are

multiply periodic of period 27: and of all functions which vanish outside a

compact ...

Page 1786

Linear operations among bounded measurable functions, I, II. I. Ann. Soc. Polon.

Math. 19, 140-161 (1946). II. ibid. 19, 161-164 (1946). On differentiation of

Linear operations among bounded measurable functions, I, II. I. Ann. Soc. Polon.

Math. 19, 140-161 (1946). II. ibid. 19, 161-164 (1946). On differentiation of

**vector**-**valued**functions. Studia Math. 11, 185-196 (1950). Continuity of**vector**-**valued**...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

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 Nauk 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