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

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Page 1176

Let p , q , kn be as in the preceding lemma , and , for each N , let X y be the

transformation in L , ( la ) which maps the

Fourier transform fn ( 5 ) into the

transform ...

Let p , q , kn be as in the preceding lemma , and , for each N , let X y be the

transformation in L , ( la ) which maps the

**vector**whose nth component has theFourier transform fn ( 5 ) into the

**vector**whose nth component has the Fouriertransform ...

Page 1178

It is plain from Plancherel's theorem that X is a bounded mapping of the space Lg

of scalar - valued functions into the space L2 ( 12 ) of square - integrable

valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , X ...

It is plain from Plancherel's theorem that X is a bounded mapping of the space Lg

of scalar - valued functions into the space L2 ( 12 ) of square - integrable

**vector**-valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , X ...

Page 1751

s differentiable m -

C ) will denote the subspaces of Ĉ ~ ( C ) consisting of all functions which are

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

...

s differentiable m -

**vector**valued functions defined in C. Similarly , © ( C ) and © (C ) will denote the subspaces of Ĉ ~ ( C ) consisting of all functions which are

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

...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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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