## Linear Operators: Spectral theory |

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Page 1176

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

transformation in L,(l,) which maps the

Fourier transform f,($) into the

transform k,($)f ...

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

transformation in L,(l,) which maps the

**vector**whose nth component has theFourier transform f,($) into the

**vector**whose nth component has the Fouriertransform k,($)f ...

Page 1837

Bicontinuous linear transformations in certain

Soc. 45, 564-569 (1939). 2. On a calculus of operators in reflerive

Trans. Amer. Math. Soc. 45, 217–234 (1939). 3. The Cauchy-Schwarz inequality

...

Bicontinuous linear transformations in certain

**vector**spaces. Bull. Amer. Math.Soc. 45, 564-569 (1939). 2. On a calculus of operators in reflerive

**vector**spaces.Trans. Amer. Math. Soc. 45, 217–234 (1939). 3. The Cauchy-Schwarz inequality

...

Page 1849

Compact metric Boolean algebras and

A. 11, 125–128 (1942). 2. On Fréchet lattices, I. J. Sci. Hirosima Univ. Ser. A. 12,

235–248 (1943). (Japanese) Math. Rev. 10, 544 (1949). 3. Remarks on a

Compact metric Boolean algebras and

**vector**lattices. J. Sci. Hirosima Univ. Ser.A. 11, 125–128 (1942). 2. On Fréchet lattices, I. J. Sci. Hirosima Univ. Ser. A. 12,

235–248 (1943). (Japanese) Math. Rev. 10, 544 (1949). 3. Remarks on a

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero