## Linear Operators, Part 2 |

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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 | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero