## Linear Operators: Spectral theory |

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Page 1178

Then 3% maps scalar-valued functions into functions with values in l,. It is plain

from Plancherel's theorem that % is a bounded mapping of the space Le of scalar

-valued functions into the space La(le) of square-integrable

Then 3% maps scalar-valued functions into functions with values in l,. It is plain

from Plancherel's theorem that % is a bounded mapping of the space Le of scalar

-valued functions into the space La(le) of square-integrable

**vector**-**valued**...Page 1751

differentiable m-

C1) 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*(CI) and Co(C1) 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

Polon. Math. 19, 140–161 (1946). II. ibid. 19, 161–164 (1946). 3. On

differentiation of

Continuity of

142 (1951). 5.

Polon. Math. 19, 140–161 (1946). II. ibid. 19, 161–164 (1946). 3. On

differentiation of

**vector**-**valued**functions. Studia Math. 11, 185–196 (1950). 4.Continuity of

**vector**-**valued**functions of bounded variation. Studia Math. 12, 133–142 (1951). 5.

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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