## Linear Operators: Spectral theory |

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Page 849

PURE AND

Edited by: R. COURANT - L. BERS - J. J. STOKER Vol. I: Supersonic Flow and

Shock Waves By R. Courant and K. O. Friedrichs Vol. II: Nonlinear Vibrations in ...

PURE AND

**APPLIED**NMATHENTATICS A Series of Texts and MonographsEdited by: R. COURANT - L. BERS - J. J. STOKER Vol. I: Supersonic Flow and

Shock Waves By R. Courant and K. O. Friedrichs Vol. II: Nonlinear Vibrations in ...

Page 945

Almost Periodic Functions The theory of compact groups developed in the

preceding section may be

analysis of the space AP of almost periodic functions on the real line R = (–oo, +

oo).

Almost Periodic Functions The theory of compact groups developed in the

preceding section may be

**applied**in an interesting and significant manner to theanalysis of the space AP of almost periodic functions on the real line R = (–oo, +

oo).

Page 1278

+ . . . --ao(t). There is an obvious sense in which such an expression can be “

whose domain is C" (but whose range is not in C", only in ...

+ . . . --ao(t). There is an obvious sense in which such an expression can be “

**applied**” to a function f, if, say, f belongs to C". Thus, we can define an operatorwhose domain is C" (but whose range is not in C", only in ...

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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